MWWpatgw>aj>Wff*iriMrwirfrniptnMnmM 


FOUR  FLAG 


UNABRIDGED  EDITION 


E.  V.  HUNTINGTON 


Conversion  Tables 


0'=0°.00000 
1'       .01666.. 

.03  333.. 

.05 

.06  666.. 

.08  333.. 

.10 

.11 666.. 

.13  333.. 

.15 

10'    0°.16666.. 
1        .18  333.. 

.20 

.21 666.. 

.23  333.. 

.25 

.26666.. 

.28  333.. 

.30 

.31 666.. 


2' 
V 
4' 
5' 
6' 
7' 
8' 
9' 


20'    0°.33  333.. 


1 
2 
3 
4 

25' 
6 
7 
8 


.51 666.. 
.53  333.. 
.55 

.56  666.. 
.58  333.. 
.60 
.61  666., 

8  .63  333., 

9  .65 
40'    0°.66  666., 


1 
2 
3 
4 

35' 
6 
7 


1 

2 

3 

4 
45' 

6 

7 

8 

9 
50' 

1 

2 

3 

4 
55' 

6 

7 

8 

9 


// 


.35 

.36666.. 
.38333.. 
.40 

.41 666.. 
.43  333.. 
.45 

.46  666.. 
9        .48333.. 
30'    0°.50 


.68  333.. 
.70 

.71 666.. 
.73  333.. 
.75 

.76  666.. 
.78  333.. 
.80 

.81 666.. 
0°.83  333.. 
.85 

.86  666.. 
.88  333.. 
.90 

.91  666.. 
.93  333.. 
.95 

.96666.. 
.98  333.. 


60'    1°.00 


0"=0°.00  000 


1" 
2" 
3" 
4" 
5" 
6" 
7" 
8" 
9" 

10" 
1 
2 
3 
4 

15" 


9 
20" 

1 

2 

3 

4 
25" 

6 

7 

8 

9 
30" 

1 

2 

3 

4 
35" 

6 

7 

8 

9 
40" 

1 

2 

3 

4 
45" 

6 

7 

8 

9 
50" 

1 

2 

3 

4 
55" 

6 

7 

8 

9 
GO" 


.00  027.. 
.00055.. 
.00  083.. 
.00  111.. 
.00 138.. 
.00 166.. 

.00 194.. 

.00222.. 

.00  25 
0°.00  277.. 

.00  305.. 

.00  333.. 

.00361.. 

.00388.. 

.00  416.. 

.00  444.. 

.00  472.. 

.00  5 

.00  527.. 
0°.00  555.. 

.00  583.. 

.00  611.. 

.00  638.. 

.00  666.. 

.00  694.. 

.00  722.. 

.00  75 

.00  777.. 

.00  805.. 
0°.00  833.. 

.00  861.. 

.00  888.. 

.00  916.. 

.00  944.. 

.00  972.. 

.01 

.01 027.. 

.01 055.. 

.01 083.. 
0°.01  111.. 

.01 138.. 

.01 166.. 

.01 194.. 

.01 222.. 

.0125 

.01 277.. 

.01 305.. 

.01 333.. 

.01 361.. 
0°.01 388.. 

.01 416.. 

.01 444.. 

.01 472.. 

.015 

.01 527.. 

.01 555.. 

.01 583.. 

.01 611.. 

.01  638.. 
0°.01666« 


1°=0.01  745  329 
l'=0.00  029  088 
1"=0.00  000  484 


radians 
8  radians 
814  radians 


1  From  Decimal  Parts  of  a 

Degree 

into  Minutes  and  Seconds 

{Exact  lvalues) 

o°.oo= 

=  0'00" 

0°.50= 

=30' 

l 

0'36" 

1 

30 '36" 

2 

112" 

2 

3112" 

3 

1'48" 

3 

31  '48" 

4 

2 '24" 

4 

32 '24" 

0°.05 

3' 

0°.55 

33' 

6 

3 '36" 

6 

33  '36" 

7 

412" 

7 

3412" 

8 

4'48" 

8 

34'48" 

9 

5 '24" 

9 

35  '24" 

0°.10 

6' 

0°.60 

36' 

1 

6'36" 

1 

36 '36" 

2 

712" 

2 

3712" 

3 

7 '48" 

3 

37 '48" 

4 

8 '24" 

4 

38 '24" 

0°.15 

9' 

0°.65 

39' 

6 

9 '36" 

6 

39'36" 

7 

1012" 

7 

4012" 

8 

10 '48" 

8 

40 '48" 

9 

11 '24" 

9 

41 '24" 

0°20 

12' 

0°.70 

42' 

1 

12 '36" 

1 

42 '36" 

2 

1312" 

2 

4312" 

3 

13 '48" 

3 

43 '48" 

4 

14'24" 

4 

44 '24" 

0°25 

15' 

0°.75 

45' 

6 

15 '36" 

6 

45 '36" 

7 

1612" 

7 

4612" 

8 

16 '48" 

8 

46 '48" 

9 

17 '24" 

9 

47 '24" 

0°.30 

18' 

0°.80 

48' 

1 

18  '36" 

1 

48 '36" 

2 

1912" 

2 

4912" 

3 

19 '48" 

3 

49 '48" 

4 

20  '24" 

4 

50 '24" 

0°.35 

21' 

0°.85 

51' 

6 

21 '36" 

6 

51 '36" 

7 

2212" 

7 

5212" 

8 

22 '48" 

8 

52 '48" 

9 

23 '24" 

9 

53 '24" 

0°.40 

24' 

0°.90 

54' 

1 

24 '36" 

1 

54  '36" 

2 

2512" 

2 

5512" 

3 

25 '48" 

3 

55 '48" 

4 

26  '24" 

4 

56 '24" 

0°.45 

27' 

0°.95 

57' 

6 

27 '36" 

6 

57 '36" 

7 

2812" 

7 

5812" 

8 

28 '48" 

8 

58  '48" 

9 

29 '24" 

9 

59 '24" 

0°.50 

30' 

r.oo 

60' 

0°.000=  0".0 

1     3".6 

2      7".2 

3    10".8 

4    14".4 

0°.005    18". 

6    21".6 

7    25".2 

8    28".8 

9    32".4 

0°.010    36". 

Decimal  Equivalents  of  Common 
Fractions 

{Exact  Values) 


06 


1/8 


3/16 


1/4 


3/8 


7/16 


1/2 


5/8 


3/4 


7/8 


1/32 


3/32 


5/32 


7/32 


9/32 


5/16 


11/32 


13/32 


1/64 
3/64 
5/64 
7/64 
9/64 
11/64 
13/64 
15/64 
17/64 
19/64 
21/64 
23/64 
25/64 
27/64 


29/64 
15/32 

31/64 


17/32 


9/16 


19/32 


21/32 


11/16 


23/32 


25/32 


13/16 


27/32 


29/32 


15/16 


31/32 


33/64 
35/64 
37/64 
39/64 
41/64 
43/64 
45/64 
47/64 
49/64 
51/64 
53/64 
55/64 
57/64 
59/64 
61/64 
63/64 


.01 5625 
.03  125 
.04  6875 
.0625 
.07  8125 
.09375 
.109375 
.12  5 
.140625 
.15  625 
.17 1875 
.1875 
.203125 
.21 875 
.23  4375 
.25 

.26  5625 
.28  125 
.29  6875 
.3125 
.32  8125 
.34375 
.35  9375 
.375 
.39  0625 
.40  625 
;42  1875 
.43  75 
.45  3125 
.46  875 
.48  4375 
.50 

.51 5625 
.53  125 
.54  6875 
.5625 
.578125 
.59375 
.609375 
.62  5 
.640625 
.65  625 
.67 1875 
.68  75 
.70  3125 
.71 875 
.73  4375 
.75 

.765625 
.78 125 
.796875 
.8125 
.82  8125 
.84375 
.85  9375 
.87  5 
.890625 
.90625 
.92  1875 
.93  75 
.95  3125 
.96  875 
.98  4375 


1  radian =57°.29578 


FOUR   PLACE   TABLES 

OF  LOGARITHMS 
AND  TRIGONOMETRIC   FUNCTIONS 

.WITH    AUXILIARY   TABLES  ( CHIEFLY   TO   THREE    FIGURES )  OF 

SQUARES,   SQUARE    ROOTS,   CUBES,    CUBE    ROOTS,    RECIPROCALS 

CIRCUMFERENCES  AND  AREAS  OF  CIRCLES,  EXPONENTIALS 

NATURAL  LOGARITHMS,  RADIANS,  AND  CONSTANTS 

3?nabribgeb  Cuttt'on 

COMPILED    BY 

E.  V.  HUNTINGTON 

ASSISTANT   PROFESSOR    OF   MATHEMATICS    IN    HARVARD   UNIVERSITY 


Descriptive  Note.  —  In  these  tables,  angles  are  expressed  in  degrees  and  decimal 
parts  of  a  degree,  instead  of  in  degrees,  minutes,  and  seconds.  A  conversion  table  is 
provided. 

All  the  values  of  any  one  function,  from  0°  to  90°,  will  be  found  at  one  opening  of 
the  book ;  there  are  also  special  tables  for  small  angles  and  angles  near  90°.  The 
arrangement  of  the  page  is  uniform,  —  the  first  figures  of  the  argument  being  given  at 
the  side  of  the  page,  and  the  last  figure  along  the  top.  Moreover,  the  function  always 
increases  reading  to  the  right,  and  decreases  reading  to  the  left,  so  that  a  frequent 
cause  of  error  in  interpolating  is  avoided. 

The  sign  J  indicates  a  point  where  the  first  figure  of  the  function  changes  in  the 
middle  of  a  line.  The  negative  characteristics,  1,  2,  etc.,  may  be  modified  into  9-10, 
8-10,  etc.,  if  preferred. 

To  facilitate  interpolation,  the  tenths  of  the  tabular  differences  are  given  at  the  end 
of  each  line,  so  that  the  actual  differences  themselves  need  not  be  considered.  In 
using  these  aids,  first  find  the  nearest  tabular  entry,  and  then  add  (to  move  to  the 
right)  or  subtract  (to  move  to  the  left),  as  the  case  may  require.  Any  interpolated 
value  may  be  in  error  by  one  unit  in  the  last  place  ;  wherever  the  errors  of  interpolation 
may  be  greater  than  this,  warning  is  given  in  the  margin. 

A  marginal  index  is  provided  throughout  the  table.  In  using  the  tabs  at  the  side  of 
the  page,  put  the  thumb  on  the  desired  tab  and  throw  the  free  pages  over ;  do  not  in- 
sert the  fingers  under  these  tabs.  The  special  tabs  at  the  upper  and  lower  edges  of  the 
page  make  it  possible  to  manipulate  the  logarithmic  part  of  the  table  entirely  with  the 
left  hand,  the  book  lying  flat  on  the  desk  ;  to  turn  forward,  insert  the  thumb  under 
the  required  tab  at  bottom  of  page;  to  turn  backward,  insert  the  finger  under  the 
required  tab  at  top  of  page. 

An  abridged  edition  is  published,  without  the  auxiliary  tables. 


FOR    SALE    BY 


THE   HARVARD   COOPERATIVE   SOCIETY 

CAMBRIDGE,   MASSACHUSETTS 

$nce,  in  flexible  clot& 60  cent* 


Copyright,  1907, 1908,  1910,  by  E.  V.  Huntington 


SOSTCM  COLuJu^z  UmiAKV 
CHESTNUT HILL,  MASS 


4 


4* 


Squares 

(Moving  the  decimal  pc 
equivalent  to  moving 

tint  ONE  place  in  n  is 
t  TWO  places  inn2) 

n 
1.0 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

1.000 

1.020 

1.040 

1.061 

1.082 

1.103 

1.124 

1.145 

1.166 

1.188 

1.210 

1.1 

1.210 

1.232 

1.254 

1.277 

1.300 

1.323 

1.346 

1.369 

1.392 

1.416 

1.440 

1.2 

1.440 

1.464 

1.488 

1.513 

1.538 

1.563 

1.588 

1.613 

1.638 

1.664 

1.690 

1.3 

1.690 

1.716 

1.742 

1.769 

1.796 

1.823 

1.850 

1.877 

1.904 

1.932 

1.960 

1.4 

1.960 

1.988 

2.016 

2.045 

2.074 

2.103 

2.132 

2.161 

2.190 

2.220 

2.250 

1.5 

2.250 

2.280 

2.310 

2.341 

2.372 

2.403 

2.434 

2.465 

2.496 

2.528 

2.560 

1.6 

2.560 

2.592 

2.624 

2.657 

2.690 

2.723 

2.756 

2.789 

2.822 

2.856 

2.890 

1.7 

2.890 

2.924 

2.958 

2.993 

3.028 

3.063 

3.098 

3.133 

3.168 

3.204 

3.240 

1.8 

3.240 

3.276 

3.312 

3.349 

3.386 

3.423 

3.460 

3.497 

3.534 

3.572 

3.610 

1.9 

3.61 

3.65 

3.69 

3.72 

3.76 

3.80 

3.84 

3.88 

3.92 

3.96 

4.00 

2.0 

4.00 

4.04 

4.08 

4.12 

4.16 

4.20 

4.24 

4.28 

4.33 

4.37 

4.41 

2.1 

4.41 

4.45 

4.49 

4.54 

4.58 

4.62 

4.67 

4.71 

4.75 

4.80 

4.84 

2.2 

4.84 

4.88 

4.93 

4.97 

5.02 

5.06 

5.11 

5.15 

5.20 

5.24 

5.29 

2.3 

5.29 

5.34 

5.38 

5.43 

5.48 

5.52 

5.57 

5.62 

5.66 

5.71 

5.76 

2.4 

5.76 

5.81 

5.86 

5.90 

5.95 

6.00 

6.05 

6.10 

6.15 

6.20 

6.25 

2.5 

6.25 

6.30 

6.35 

6.40 

6.45 

6.50 

6.55 

6.60 

6.66 

6.71 

6.76 

2.6 

6.76 

6.81 

6.86 

6.92 

6.97 

7.02 

7.08 

7.13 

7.18 

7.24 

7.29 

2.7 

7.29 

7.34 

7.40 

7.45 

7.51 

7.56 

7.62 

7.67 

7.73 

7.78 

7.84 

2.8 

7.84 

7.90 

7.95 

8.01 

8.07 

8.12 

8.18 

8.24 

8.29 

8.35 

8.41 

2.9 

8.41 

8.47 

8.53 

8.58 

8.64 

8.70 

8.76 

8.82 

8.88 

8.94 

9.00 

3.0 

9.00 

9.06 

9.12 

9.18 

9.24 

9.30 

9.36 

9.42 

9.49 

9.55 

9.61 

3.1 

9.61 

9.67 

9.73 

9.80 

9.86 

9.92 

9.99 

10.05 

10.11 

10.18 

10.24 

3.2 

10.24 

10.30 

1037 

10.43 

10.50 

10.56 

10.63 

10.69 

10.76 

10.82 

10.89 

3.3 

10.89 

10.96 

11.02 

11.09 

11.16 

11.22 

11.29 

11.36 

11.42 

11.49 

11.56 

3.4 

11.56 

11.63 

11.70 

11.76 

11.83 

11.90 

11.97 

12.04 

12.11 

12.18 

12.25 

3.5 

12.25 

12.32 

12.39 

12.46 

12.53 

12.60 

12.67 

12.74 

12.82 

12.89 

12.96 

3.6 

12.96 

13.03 

13.10 

13.18 

13.25 

13.32 

13.40 

13.47 

13.54 

13.62 

13.69 

3.7 

13.69 

13.76 

13.84 

13.91 

13.99 

14.06 

14.14 

14.21 

14.29 

14.36 

14.44 

3.8 

14.44 

14.52 

14.59 

14.67 

14.75 

14.82 

14.90 

14.98 

15.05 

15.13 

15.21 

3.9 

15.21 

15.29 

15.37 

15.44 

15.52 

15.60 

15.68 

15.76 

15.84 

15.92 

16.00 

4.0 

16.00 

16.08 

16.16 

16.24 

16.32 

16.40 

16.48 

16.56 

16.65 

16.73 

16.81 

4.1 

16.81 

16.89 

16.97 

17.06 

17.14 

17.22 

17.31 

17.39 

17.47 

17.56 

17.64 

4.2 

17.64 

17.72 

17.81 

17.89 

17.98 

18.06 

18.15 

18.23 

18.32 

18.40 

18.49 

4.3 

18.49 

18.58 

18.66 

18.75 

18.84 

18.92 

19.01 

19.10 

19.18 

19.27 

19.36 

4.4 

19.36 

19.45 

19.54 

19.62 

19.71 

19.80 

19.89 

19.98 

20.07 

20.16 

20.25 

4.5 

20.25 

20.34 

20.43 

20.52 

20.61 

20.70 

20.79 

20.88 

20.98 

21.07 

21.16 

4.6 

21.16 

21.25 

21.34 

21.44 

21.53 

21.62 

21.72 

21.81 

21.90 

22.00 

22.09 

4.7 

22.09 

22.18 

22.28 

22.37 

22.47 

22.56 

22.66 

22.75 

22.85 

22.94 

23.04 

4.8 

23,04 

23.14 

23.23 

23.33 

23.43 

23.52 

23.62 

23.72 

23.81 

23.91 

24.01 

4.9 

24.01 

24.11 

24.21 

24.30 

24.40 

24.50 

24.60 

24.70 

24.80 

24.90 

25.00 

5.0 

25.00 

25.10 

25.20 

25.30 

25.40 

25.50 

25.60 

25.70 

25.81 

25.91 

26.01 

5.1 

26.01 

26.11 

26.21 

26.32 

26.42 

26.52 

26.63 

26.73 

26.83 

26.94 

27.04 

5.2 

27.04 

27.14 

27.25 

27.35 

27.46 

27.56 

27.67 

27.77 

27.88 

27.98 

28.09 

5.3 

28.09 

28.20 

28.30 

28.41 

28.52 

28.62 

28.73 

28.84 

28.94 

29.05 

29.16 

5.4 

29.16 

29.27 

29.38 

29.48 

29.59 

29.70 

29.81 

29.92 

30.03 

30.14 

30.25 

5.5 

30.25 

30.36 

30.47 

30.58 

30.69 

30.80 

30.91 

31.02 

31.14 

31.25  ' 

31.36 

5.6 

31.36 

31.47 

31.58 

31.70 

31.81 

31.92 

32.04 

32.15 

32.26 

32.38 

32.49 

5.7 

32.49 

32.60 

32.72 

32.83 

32.95 

33.06 

33.18 

33.29 

33.41 

33.52 

33.64 

5.8 

33.64 

33.76 

33.87 

33.99 

34.11 

34.22 

34.34 

34.46 

34.57 

34.69 

34.81 

5.9 

34.81 

34.93 

35.05 

35.16 

35.28 

35.40 

35.52 

35.64 

35.76 

35.88 

36.00 

6. 

36.0 

37.2 

38.4 

39.7 

41.0 

42.3 

43.6 

44.9 

46.2 

47.6 

49.0 

7. 

49.0 

50.4 

51.8 

53.3 

54.8 

56.3 

57.8 

59.3 

60.8 

62.4 

64.0 

8. 

64.0 

65.6 

67.2 

68.9 

70.6 

72.3 

74.0 

75.7 

77.4 

79.2 

81.0 

9. 

81.0 

82.8 

84.6 

86.5 

88.4 

90.3 

92.2 

94.1 

96.0 

98.0 

100.0 

Tenths  of  the 
Tabular  Difference 

12    3    4    5 

2  4  6    810 

2  5  7   911 

2  5  7  10  12 

3  5  8  11  13 
3  6  9  12  14 

3  6    9  12  15 

3  7  10  13  16 

3  7  10  14  17 

4  7  11  15  18 
0  112   2 


1  2 

1  2 

1  2 

1  2 

1  2 

1  2 

1  2 

1  2 

1  2 

1  2 


1  2 

1  2 

1  2 

1  2 

1  2 


2  2 

2  2 

2  2 

2  2 

2  2 

2  3 

2  3 

2  3 

2  3 

2  3 


2 
2 
2 
2 
2 

2 
2 
2 
2 
2 

2  3  4 

2  3  4 

3  3  4 
3  3  4 
3  4  4 


tt2  =  9.870 


(2) 


1/V  =  0.10132 


O'NEILL  LIBRARY 
BOSTON  CO 


Square 

Roots 

(Moving  the  decimal  point  TWO  places  in  n  is 
equivalent  to  moving  it  ONE  place  in  */7i) 

Ta 
i 

l 
l 
l 
l 
l 

rent 
iula 

2 

3 

2 
2 
2 
1 

hs  of  the 

r  Difference 

3   4   5 

n 

.1 

.2 
.3 
.4 

0 

l 

2 

3 

4 

5 

6 

7 

8         9 

10 

.316 

.447 
.548 
.632 

.332 

.458 
.557 
.640 

.346 

.469 
.566 
.648 

.361 

.480 
.574 
.656 

.374 

.490 
.583 
.663 

.387 
.387 
.500 
.592 
.671 

.400 
.510 
.600 
.678 

.412 
.520 
.608 
.686 

.424     .436 
.529     .539 
.616     .624 
.693     .700 

.447 
.548 
.632 
.707 

4  6  7 
4  5  6 
3  4  5 
3  3  4 
2    3    4 

.5 

.6 

17 
.8 
.9 

.707 
.775 
.837 
.894 
0.949 

.714 
.781 
.843 
.900 
0.954 

.721 
.787 
.849 
.906 
0.959 

.728 
.794 
.854 
.911 
0.964 

.735 
.800 
.860 
.917 
0.970 

.742 
.806 
.866 
.922 
0.975 

.748 
.812 
.872 
.927 
0.980 

.755 
.819 
.877 
.933 
0.985 

.762     .768 
.825     .831 
.883     .889 
.938     .943 
0.990  0.995 

.775 

.837 

.894 

0.949 

1.000 

l 
l 
l 
l 
l 

1 

1 
1 

1 
1 

2  3  3 
2  2  3 
2  2  3 
2  2  3 
2    2    3 

1.0 

1.1 

1.2 
1.3 
1.4 

1.000 
1.049 
1.095 
1.140 
1.183 

1.005 
1.054 
1.100 
1.145 
1.187 

1.010 
1.058 
1.105 
1.149 
1.192 

1.015 
1.063 
1.109 
1.153 
1.196 

1.020 
1.068 
1.114 
1.158 
1.200 

1.025 
1.072 
1.118 
1.162 
1.204 

1.030 
1.077 
1.122 
1.166 
1.208 

1.034 
1.082 
1.127 
1.170 
1.212 

1.039   1.044 
1.0S6   1.091 
1.131   1.136 
1.175   1.179 
1.217   1.221 

1.049 
1.095 
1.140 
1.183 
1.225 

0 
0 
0 
0 
0 

1 
1 
1 
1 
1 

12  2 
12  2 
12  2 
12  2 
12    2 

1.5 

1,6 
1.7 
1.8 
1.9 

1.225 
1.265 
1.304 
1.342 
1.378 

1.229 
1.269 
1.308 
1.345 
1.382 

1.233 
1.273 
1.311 
1.349 
1.386 

1.237 
1.277 
1.315 
1.353 
1.389 

1.241 
1.281 
1.319 
1.356 
1.393 

1.245 
1.285 
1.323 
1.360 
1.396 

1.249 
1.288 
1.327 
1.364 
1.400 

1.253 
1.292 
1.330 
1.367 
1.404 

1.257   1.261 
U.296   1.300 
1.334   1.338 
1.371   1.375 
1.407   1.411 

1.265 
1.304 
1.342 
1.378 
1.414 

0 
0 
0 
0 
0 

1 

1 
1 
1 
1 

12  2 
12  2 
12  2 
112 
112 

2.0 

2.1 
2.2 
2.3 

2.4 

1.414 
1.449 
1.483 
1.517 
1.549 

1.418 
1.453 
1.487 
1.520 
1.552 

1.421 
1.456 
1.490 
1.523 
1.556 

1.425 
1.459 
1.493 
1.526 
1.559 

1.428 
1.463 
1.497 
1.530 
1.562 

1.432 
1.466 
1.500 
1.533 
1.565 

1.435 
1.470 
1.503 
1.536 
1.568 

1.439 
1.473 
1.507 
1.539 
1.572 

1.442   1.446 
1.476   1.480 
1.510   1.513 
1.543    1.546 
1.575   1.578 

1.449 
1.483 
1.517 
1.549 
1.581 

0 
0 
0 
0 
0 

1 
1 

1 
1 
1 

112 
112 
112 
112 
112 

2.5 
2.6 
2.7 
2.8 
2.9 

1.581 
1.612 
1.643 
1.673 
1.703 

1.584 
1.616 
1.646 
1.676 
1.706 

1.587 
1.619 
1.649 
1.679 
1.709 

1.591 
1.622 
1.652 
1.682 
1.712 

1.594 
1.625 
1.655 
1.685 
1.715 

1.597 
1.628 
1.658 
1.688 
1.718 

1.600 
1.631 
1.661 
1.691 
1.720 

1.603 
1.634 
1.664 
1.694 
1.723 

1.606   1.609 
1.637   1.640 
1.667   1.670 
1.697   1.700 
1.726   1.729 

1.612 
1.643 
1.673 
1.703 
1.732 

0 
0 
0 
0 
0 

1 

1 
1 
1 
1 

112 
112 
112 
111 
111 

3.0 

3.1 
3.2 
3.3 
3.4 

1.732 
1.761 
1.789 
1.817 
1.844 

1.735 
1.764 
1.792 
1.819 
1.847 

1.738 
1.766 
1.794 
1.822 
1.849 

1.741 
1.769 
1.797 
1.825 
1.852 

1.744 
1.772 
1.800 
1.828 
1.855 

1.746 
1.775 
1.803 
1.830 

1.749 
1.778 
1.806 
1.833 
1.860 

1.752 
1.780 
1.808 
1.836 
1.863 

1.755   1.758 
1.783   1.786 
1.811   1.814 
1.838   1.841 
1.865    1.868 

1.761 
1.789 
1.817 
1.844 
1.871 

0 
0 
0 
0 
0 

1 

1 
1 
1 
1 

111 
111 
111 
111 

1.857 

111 

3.5 
3.6 
3.7 
3.8 
3.9 

1.871 
1.897 
1.924 
1.949 
1.975 

1.873 
1.900 
1.926 
1.952 
1.977 

1.876 
1.903 
1.929 
1.954 
1.980 

1.879 
1.905 
1.931 
1.957 
1.982 

1.881 
1.908 
1.934 
1.960 
1.985 

1.884 
1.910 
1.936 
1.962 
1.987 

1.887 
1.913 
1.939 
1.965 
1.990 

1.889 
1.916 
1.942 
1.967 
1.992 

1.892   1.895 
1.918   1.921 
1.944   1.947 
1.970   1.972 
1.995   1.997 

1.897 
1.924 
1.949 
1.975 
2.000 

0 
0 
0 
0 
0 

1 
1 
1 
1 
1 

111 
111 
111 
111 
111 

4.0 

4.1 
4.2 
4.3 
4.4 

2.000 
2.025 
2.049 
2.074 
2.098 

2.002 
2.027 
2.052 
2.076 
2.100 

2.005 
2.030 
2.054 
2.078 
2.102 

2.007 
2.032 
2.057 
2.081 
2.105 

2.010 
2.035 
2.059 
2.083 
2.107 

2.012 
2.037 
2.062 
2.086 
2.110 

2.015 
2.040 
2.064 
2.088 
2.112 

2.017 
2.042 
2.066 
2.090 
2.114 

2.020  2.022 
2.045   2.047 
2.069  2.071 
2.093   2.095 
2.117  2.119 

2.025 
2.049 
2.074 
2.098 
2.121 

0 
0 
0 
0 
0 

0 
0 
0 
0 
0 

111 
111 
111 
111 
111 

4.5 
4.6 
4.7 
4.8 
4.9 

2.121 
2.145 
2.168 
2.191 
2.214 

2.124 
2.147 
2.170 
2.193 
2.216 

2.126 
2.149 
2.173 
2.195 
2.218 

2.128 
2.152 
2.175 
2.198 
2.220 

2.131 
2.154 
2.177 
2.200 
2.223 

2.133 
2.156 
2.179 
2.202 
2.225 

2.135 
2.159 
2.182 
2.205 
2.227 

2.138 
2.161 
2.184 
2.207 
2.229 

2.140  2.142 
2.163   2.166 
2.186  2.189 
2.209  2.211 
2.232  2.234 

2.145 
2.168 
2.191 
2.214 
2.236 

0 
0 
0 
0 
0 

0 
0 
0 
0 
0 

111 
111 
111 
111 
111 

5. 
6. 
7. 

8. 

, 

2.236 
2.449 
2.646 
2.828 
3.000 

2.258 
2.470 
2.665 
2.846 
3.017 

2.280 
2.490 
2.683 
2.864 
3.033 

2.302 
2.510 
2.702 
2.881 
3.050 

2.324 
2.530 
2.720 
2.898 
3.066 

2.345 
2.550 
2.739 
2.915 
3.082 

2.366 
2.569 
2.757 
2.933 
3.098 

2.387 
2.588 
2.775 
2.950 
3.114 

2.408  2.429 
2.608  2.627 
2.793   2.811 
2.966  2.983 
3.130  3.146 

2.449 
2.646 
2.828 
3.000 
3.162 

2 
2 
2 
2 
2 

4 
4 
4 
3 
3 

6  9  11 
6  8  10 
5  7  9 
5  7  9 
5    6    8 

wc%$ 


r.05 


W 


<* 


^  =  1.772454 


(3) 


n/i/7t  =  0.56419 


1$ 


Cubes 

(Moving  the  decimal  point  ONE  place  in  n  la 
equivalent  to  moving  it  THREE  places  in  ttZ) 

Tenths  c 
Tabular  Di 

12    3 

3  7  10 

4  8  12 

5  9  14 
5  11  16 
112 

f  the 

n 

1.0 

1.1 
1.2 
1.3 
1.4 

0 

12        3        4 

5 

6         7         8        9 

10 

ffennci 

4   5 

1.000 
1.331 
1.728 
2.197 
2.74 

1.030  1.061   1.093   1.125 
1.368   1.405    1.443    1.482 
1.772   1.816  1.861   1.907 
2.248  2.300  2.353  2.406 
2.80     2.86     2.92     2.99 

1.158 
1.521 
1.953 
2.460 
3.05 

1.191   1.225    1.260   1.295 
1.561   1.602   1.643   1.685 
2.000  2.048  2.097  2.147 
2.515  2.571  2.628  2.686 
3.11     3.18     3.24     3.31 

1.331 
1.728 
2.197 
2.744 
3.38 

13  17 
16  20 
19  23 
22  27 
3   3 

1.5 
1.6 
1.7 
1.8 
1.9 

3.38 
4.10 
4.91 
5.83 
6.86 

3.44     3.51     3.58     3.65 
4.17     4.25     4.33     4.41 
5.00     5.09     5.18     5.27 
5.93     6.03     6.13     6.23 
6.97     7.08     7.19     7.30 

3.72 
4.49 
5.36 
6.33 
7.41 

3.80     3.87     3.94     4.02 
4.57     4.66     4.74     4.83 
5.45     5.55     5.64     5.74 
6.43     6.54     6.64     6.75 
7.53     7.65     7.76     7.88 

4.10 
4.91 
5.83 
6.86 
8.00 

1 
1 

1 
1 
1 

1 
2 
2 
2 
2 

2 
2 
3 
3 
3 

3   4 

3  4 

4  5 

4  5 

5  6 

2.0 

2.1 
2.2 
2.3 
2.4 

8.00 

9.26 

10.65 

12.17 

13.82 

8.12     8.24     8.37     8.49 

9.39     9.53     9.66     9.80 

10.79  10.94   11.09   11.24 

12.33    12.49   12.65    12.81 

14.00   14.17   14.35   14.53 

8.62 

9.94 

11.39 

12.98 

14.71 

8.74     8.87     9.00     9.13 
10.08   10.22   10.36   10.50 
11.54   11.70   11.85   12.01 
13.14   13.31    13.48   13.65 
14.89   15.07   15.25   15.44 

9.26 
10.65 
12.17 
13.82 
15.62 

1 
1 
2 
2 
2 

3 
3 
3 
3 

4 

4 
4 
5 
5 
5 

5  6 

6  7 

6  8 

7  8 
7   9 

2.5 
2.6 
2.7 
2.8 
2.9 

15.62 
17.58 
19.68 
21.95 
24.39 

15.81   16.00   16.19   16.39 
17.78   17.98   18.19  18.40 
19.90  20.12   20.35   20.57 
22.19  22.43   22.67  22.91 
24.64  24.90  25.15   25.41 

16.58 
18.61 
20.80 
23.15 
25.67 

16.78   16.97   17.17   17.37 
18.82   19.03   19.25    19.47 
21.02   21.25   21.48   21.72 
23.39  23.64  23.89  24.14 
25.93  26.20  26.46  26.73 

17.58 
19.68 
21.95 
24.39 
27.00 

2 
2 
2 
2 
3 

4 
4 
5 
5 
5 

6    8  10 

6  8  11 

7  9  11 

7  10  12 

8  10  13 

3.0 
3.1 
3.2 
3.3 

3.4 

27.0 
29.8 
32.8 
35.9 
39.3 

27.3     27.5     27.8     28.1 
30.1     30.4     30.7     31.0 
33.1     33.4     33.7     34.0 
36.3     36.6     36.9     37.3 
39.7     40.0     40.4     40.7 

28.4 
31.3 
34.3 
37.6 
41.1 

28.7     28.9     29.2     29.5 
31.6     31.9     32.2     32.5 
34.6     35.0     35.3     35.6 
37.9     38.3     38.6     39.0 
41.4     41.8     42.1     42.5 

29.8 
32.8 
35.9 
39.3 
42.9 

0 
0 
0 
0 
0 

1 

1 
1 
1 
1 

1 

1 
1 
1 
1 

1    1 
1    1 
1    2 
1    2 
1    2 

3.5 
3.6 
3.7 
3.8 
3.9 

42.9 
46.7 
50.7 
54.9 
59.3 

43.2  43.6     44.0     44.4 

47.0  47.4     47.8     48.2 

51.1  51.5     51.9     52.3 

55.3  55.7     56.2     56.6 
59.8     60.2     60.7     61.2 

44.7 
48.6 
52.7 
57.1 
61.6 

45.1  45.5     45.9     46.3 

49.0  49.4     49.8     50.2 

53.2  53.6     54.0     54.4 
57.5     58.0     58.4     58.9 

62.1  62.6     63.0     63.5 

46.7 
50.7 
54.9 
59.3 
64.0     ! 

0 
0 
0 
0 
0 

1 
1 

1 
1 
1 

1 
1 
1 
1 
1 

2    2 
2    2 
2    2 
2    2 
2    2 

4.0 

4.1 
4.2 
4.3 

4.4 

64.0 
68.9 
74.1 
79.5 
85.2 

64.5  65.0     65.5     65.9 
69.4     69.9     70.4     71.0 

74.6  75.2     75.7     76.2 
80.1     80.6     81.2     81.7 
85.8     86.4     86.9     87.5 

66.4 
71.5 
76.8 
82.3 
88.1 

66.9     67.4     67.9     68.4 
72.0     72.5     73.0     73.6 
77.3     77.9     78.4     79.0 
82.9     83.5     84.0     84.6 
88.7     89.3     89.9     90.5 

68.9     ! 

74.1 

79.5 

85.2 

91.1 

0 

1 
1 
1 
1 

1 
1 
1 
1 
1 

1 

2 
2 
2 
2 

2    2 
2    3 
2    3 
2    3 
2    3 

4.5 
4.6 
4.7 
4.8 
4.9 

91.1 

97.3 

103.8 

110.6 

117.6 

91.7     92.3     93.0     93.6 

98.0     98.6     99.3     99.9 

104.5   105.2   105.8   106.5 

111.3  112.0   112.7   113.4 

118.4  119.1   119.8   120.6 

94.2 
100.5 
107.2 
114.1 
121.3 

94.8     95.4     96.1     96.7 
101.2   101.8   102.5    103.2 
107.9   108.5    109.2   109.9 
114.8   115.5   116.2   116.9 
122.0   122.8   123.5    124.3 

97.3 
103.8 
110.6 
117.6 
125.0 

1 
1 
1 

1 
1 

1 
1 
1 

1 

1 

2 

2 
2 
2 
2 

2  3 

3  3 
3   3 
3   4 

3    4 

5.0 

5.1 
5.2 
5.3 

5.4 

125.0 
132.7 
140.6 
148.9 
157.5 

125.8   126.5   127.3   128.0 
133.4   134.2   135.0   135.8 
141.4   142.2   143.1   143.9 
149.7   150.6   151.4   152.3 
158.3   159.2   160.1   161.0 

128.8 
136.6 
144.7 
153.1 
161.9 

129.6   130.3   131.1    131.9 

137.4  138.2   139.0   139.8 

145.5  146.4   147.2   148.0 
154.0   154.9   155.7   156.6 
162.8   163.7   164.6   165.5 

132.7 
140.6 
148.9 
157.5 
166.4 

1 

1 
1 
1 
1 

2 
2 
2 
2 
2 

2 
2 
2 
3 
3 

3    4 
3   4 
3   4 

3  4 

4  4 

5.5 
5.6 
5.7 
5.8 
5.9 

166.4 
175.6 
185.2 
195.1 
205.4 

167.3  168.2    169.1   170.0 
176.6   177.5   178.5   179.4 
186.2   187.1    188.1   189.1 
196.1   197.1    198.2   199.2 

206.4  207.5   208.5   209.6 

171.0 
180.4 
190.1 
200.2 
210.6 

171.9   172.8   173.7   174.7 
181.3    182.3   183.3   184.2 

191.1  192.1   193.1   194.1 

201.2  202.3   203.3   204.3 
211.7  212.8  213.8  214.9 

175.6 
185.2 
195.1 
205.4     1 
216.0 

1 

1 
1 

1 
1 

2 
2 
2 
2 
2 

3 
3 
3 
3 
3 

4   5 
4   5 
4   5 
4   5 
4   5 

6. 

7. 

8. 
9. 

216. 

343. 
512. 
729. 

227.     238.     250.     262. 

358.     373.     389.     405. 
531.     551.     572.     593. 
754.     779.     804.     831. 

275. 
275. 
422. 
614. 
857. 

287.     301.     314.     329. 
439.     457.     475.     493. 
636.     659.     681.     705. 
885.     913.     941.     970. 

343. 
512. 
729. 
1000. 

1 

1 
2 
2 
3 

2 
3 
3 
4 

5 

4 
4 
5 
7 
8. 

5    6 
5    7 
7    8 
911 
LI  14 

7T3  =  3U)06 

(4) 

1/7T3  =  0.032252 

Cube  Roots 

(Moving  the  decimal  point  THREE  places  in  n 
is  equivalent  to  moving  it  ONE  place  in  £/Ti) 

Tenths  of  the 
Tabular  Difference 

n 

.010 

0 

1 

2 

3 

4 

5 

6         7 

8 

9 

10 

1    2 

1    1 

3    4    5 

.2154 

.2162 

.2169 

.2176 

.2183 

.2190 

.2197   .2204 

.2210 

.2217 

.2224 

2    3    3 

.011 

.2224 

.2231 

.2237 

.2244 

.2251 

.2257 

.2264   .2270 

.2277 

.2283 

.2289 

1    1 

2   3    3 

.012 

.2289 

.2296 

.2302 

.2308 

.2315 

.2321 

.2327   .2333 

.2339 

.2345 

.2351 

1    1 

2   2   3 

.013 

.2351 

.2357 

.2363 

.2369 

.2375 

.2381 

.2387   .2393 

.2399 

.2404 

.2410 

1    1 

2    2    3 

.014 

.2410 

.2416 

.2422 

.2427 

.2433 

.2438 

.2444   .2450 

.2455 

.2461 

.2466 

1    1 

2    2    3 

.015 

.2466 

.2472 

.2477 

.2483 

.2488 

.2493 

.2499   .2504 

.2509 

.2515 

.2520 

1    1 

2    2    3 

.016 

.2520 

.2525 

.2530 

.2535 

.2541 

.2546 

.2551   .2556 

.2561 

.2566 

.2571 

1    1 

2    2    3 

.017 

.2571 

.2576 

.2581 

.2586 

.2591 

.2596 

.2601   .2606 

.2611 

.2616 

.2621 

0    1 

12    2 

.018 

.2621 

.2626 

.2630 

.2635 

.2640 

.2645 

.2650   .2654 

.2659 

.2664 

.2668 

0    1 

12    2 

.019 

.2668 

.2673 

.2678 

.2682 

.2687 

.2692 

.2696   .2701 

.2705 

.2710 

.2714 

0    1 

12    2 

.020 

.2714 

.2719 

.2723 

.2728 

.2732 

.2737 

.2741   .2746 

.2750 

.2755 

.2759 

0    1 

12    2 

.021 

.2759 

.2763 

.2768 

.2772 

.2776 

.2781 

.2785   .2789 

.2794 

.2798 

.2802 

0    1 

12    2 

.022 

.2802 

.2806 

.2811 

.2815 

.2819 

.2823 

.2827  .2831 

.2836 

.2840 

.2844 

0    1 

12    2 

.023 

.2844 

.2848 

.2852 

.2856 

.2860 

.2864 

.2868   .2872 

.2876 

.2880 

.2884 

0    1 

12    2 

.024 

.2884 

.2888 

.2892 

.2896 

.2900 

.2904 

.2908   .2912 

.2916 

.2920 

.2924 

0    1 

12    2 

.025 

.2924 

.2928 

.2932 

.2936 

.2940 

.2943 

.2947   .2951 

.2955 

.2959 

.2962 

0    1 

12    2 

.026 

.2962 

.2966 

.2970 

.2974 

.2978 

.2981 

.2985    .2989 

.2993 

.2996 

3000 

0    1 

12    2 

.027 

.3000 

.3004 

.3007 

.3011 

.3015 

.3018 

.3022   .3026 

.3029 

.3033 

.3037 

0    1 

112 

.028 

.3037 

.3040 

.3044 

.3047 

.3051 

.3055 

.3058   .3062 

.3065 

.3069 

.3072 

0    1 

112 

.029 

.3072 

.3076 

.3079 

.3083 

.3086 

.3090 

.3093   .3097 

3100 

.3104 

.3107 

0    1 

112 

.03 

.311 

.314 

.317 

.321 

.324 

.327 

.330     .333 

336 

.339 

342 

0    1 

112 

.04 

.342 

.345 

.348 

.350 

.353 

.356 

.358     .361 

.363 

.366 

368 

0    1 

111 

.05 

.368 

.371 

.373 

.376 

.378 

.380 

.383     .385 

387 

.389 

391 

0   0 

111 

.06 

.391 

.394 

.396 

.398 

.400 

.402 

.404     .406 

.408 

.410 

.412 

0   0 

111 

.07 

.412 

.414 

.416 

.418 

.420 

.422 

.424     .425 

.427 

.429 

.431 

0    0 

111 

.08 

.431 

.433 

.434 

.436 

.438 

.440 

.441     .443 

.445 

.446 

.448 

0    0 

111 

.09 

.448 

.450 

.451 

.453 

.455 

.456 

.458     .459 

.461 

.463 

.464 

0   0 

Oil 

.1 

.464 

.479 

.493 

.507 

.519 

.531 

1    3 

4    5    7 

.531 

.543     .554 

.565 

.575 

.585 

1    2 

3    4    5 

.2 

.585 

.594 

.604 

.613 

.621 

.630 

.638     .646 

.654 

.662 

.669 

1    2 

3    3    4 

.3 

.669 

.677 

.684 

.691 

.698 

.705 

.711     .718 

.724 

.731 

.737 

1    1 

2   3    3 

.4 

.737 

.743 

.749 

.755 

.761 

.766 

.772     .777 

.783 

.788 

.794 

1    1 

2    2    3 

.5 
.6 

.794 
.843 

.799 
.848 

.804 
.853 

.809 
.857 

.814 

.819 

.824     .829 
.871     .875 

.834 
.879 

.839 
.884 

.843 
.888 

0    1 
0    1 

12    2 

.862 

.866 

12    2 

.7 

.888 

.892 

.896 

.900 

.905 

.909 

.913     .917 

.921 

.924 

.928 

0    1 

12    2 

.8 

.928 

.932 

.936 

.940 

.944 

.947 

.951     .955 

.958 

.962 

0.965 

0    1 

112 

.9 

0.965 

0.969 

0.973 

0.976 

0.980 

0.983 

0.986  0.990 

0.993 

0.997 

1.000 

0    1 

112 

1.0 

1.000 

1.003 

1.007 

1.010 

1.013 

1.016 

1.020   1.023 

1.026 

1.029 

1.032 

0    1 

112 

1.1 

1.032 

1.035 

1.038 

1.042 

1.045 

1.048 

1.051    1.054 

1.057 

1.060 

1.063 

0    1 

112 

1.2 

1.063 

1.066 

1.069 

1.071 

1.074 

1.077 

1.080   1.083 

1.086 

1.089 

1.091 

0    1 

111 

1.3 

1.091 

1.094 

1.097 

1.100 

1.102 

1.105 

1.108   1.111 

1.113 

1.116 

1.119 

0    1 

111 

1.4 

1.119 

1.121 

1.124 

1.127 

1.129 

1.132 

1.134   1.137 

1.140 

1.142 

1.145 

0    1 

111 

1.5 

1.145 

1.147 

1.150 

1.152 

1.155 

1.157 

1.160   1.162 

1.165 

1.167 

1.170 

0   0 

111 

1.6 

1.170 

1.172 

1.174 

1.177 

1.179 

1.182 

1.184   1.186 

1.189 

1.191 

1.193 

0    0 

111 

1.7 

1.193 

1.196 

1.198 

1.200 

1.203 

1.205 

1.207   1.210 

1.212 

1.214 

1.216 

0    0 

111 

1.8 

1.216 

1.219 

1.221 

1.223 

1.225 

1.228 

1.230   1.232 

1.234 

1.236 

1.239 

0    0 

111 

1.9 

1.239 

1.241 

1.243 

1.245 

1.247 

1.249 

1.251    1.254 

1.256 

1.258 

1.260 

0   0 

111 

2. 

1.260 

1.281 

1.301 

1.320 

1.339 

1.357 

2   4 

6    8  10 

1.357 

1.375    1.392 

1.409 

1.426 

1.442 

2    3 

5    7    9 

3. 

1.442 

1.458 

1.474 

1.489 

1.504 

1.518 

1.533   1.547 

1.560 

1.574 

1.587 

1    3 

4    6    7 

4. 

1.587 

1.601 

1.613 

1.626 

1.639 

1.651 

1.663   1.675 

1.687 

1.698 

1.710 

1    2 

4   5    6 

5. 

1.710 

1.721 

1.732 

1.744 

1.754 

1.765 

1.776   1.786 

1.797 

1.807 

1.817 

1    2 

3   4   5 

6. 

1.817 

1.827 

1.837 

1.847 

1.857 

1.866 

1.876   1.885 

1.895 

1.904 

1.913 

1    2 

3    4   5 

7. 

1.913 

1.922 

1.931 

1.940 

1.949 

1.957 

1.966   1.975 

1.983 

1.992 

2.000 

1    2 

3   3   4 

8. 

2.000 

2.008 

2.017 

2.025 

2.033 

2.041 

2.049  2.057 

2.065 

2.072 

2.080 

1    2 

2   3   4 

9. 

2.080 

2.088 

2.095 

2.103 

2.110 

2.118 

2.125   2.133 

2.140 

2.147 

2.154 

1    1 

2   3   4 

^7T  =  1.46459 


(5) 


0.68278  f/b/Tt  =  1.24070 


r.v 


d& 


0s 


W 


<* 


o°2 


TTTi 

1     Circumferences  of  Circles 

(n  =  diam.} 

Tenths  of  the 

ft 

1. 
2. 

3! 

4. 

5. 
6. 
4. 

8. 
9. 

0 

12         3         4 

5 

6         7         8 

9 

10 

Tabular  Difference 

12    3    4    5 

3.14 

6.28 

9.42 

12.57 

15.71 
18.85 
21.99 
25.13 
2827 

3.46     3.77     4.08     4.40 

6.60     6.91     7.23     7.54 

9.74   10.05    10.37   10.68 

12.88   13.19   13.51   13.82 

16.02   16.34   16.65    16.96 
19.16    19.48    19.79   20.11 
22.31   22.62   22.93   23.25 
25.45   25.76   26.08   26.39 
28.59  28.90   29.22   29.53 

4.71 

7.85 

11.00 

14.14 

1728 
20.42 
23.56 
26.70 
29.85 

5.03     5.34     5.65 

8.17     8.48     8.80 

11.31    11.62    11.94 

14.45    14.77   15.08 

17.59   17.91   18.22 
20.73   21.05   21.36 
23.88   24.19  24.50 
27.02   27.33   27.65 
30.16  30.47   30.79 

5.97 

9.11 

12.25 

15.39 

18.54 
21.68 
24.82 
27.96 
31.10 

6.28 

9.42 

12.57 

15.71 

18.85 
21.99 
25.13 
28.27 
31.42 

3    6    9  13  16 
3    6    9  13  16 
3    6    9  13  16 
3    6    9  13  16 

3    6    9  13  16 
3    6    9  13  16 
3    6    9  13  16 
3    6    9  13  16 
3    6    9  13  16 

1  —  m^     A  i-anr  /-vf  /""',i*»/-»l£io  ( *n        A 1 n  mi  ~\  (Moving  the  decimal  point  OJTE  place  inn  is 

4;7rM-  /\reas  01  circles  yn  —  aiain.)  equivalent  to  moving  it  two  places  in  irn2/^.)    Tenths  of  the 


Tabular  Difference 

n 
1.0 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

1 

2    3    4    5 

0.785 

0.801 

0.817 

0.833 

0.849 

0.866 

0.882 

0.899 

0.916 

0.933 

0.950 

2 

3    5    7    9 

1.1 

0.950 

0.968 

0.985 

1.003 

1.021 

1.039 

1.057 

1.075 

1.094 

1.112 

1.131 

2 

4    5    7    9 

L2 

1.131 

1.150 

1.169 

1.188 

1208 

1.227 

1.247 

1.267 

1.287 

1.307 

1327 

2 

4    6    810 

L3 

1.327 

1.348 

1.368 

1.389 

1.410 

1.431 

1.453 

1.474 

1.496 

1.517 

1.539 

2 

4   6    811 

1.4 

1.539 

1.561 

1.584 

1.606 

1.629 

1.651 

1.674 

1.697 

1.720 

1.744 

1.767 

2 

5    7    911 

1.5 

1.767 

1.791 

1.815 

1.839 

1.863 

1.887 

1.911 

1.936 

1.961 

1.986 

2.011 

2 

5    7  10  12 

1.6 

2.011 

2.036 

2.061 

2.087 

2.112 

2.138 

2.164 

2.190 

2.217 

2.243 

2.270 

3 

5    8  10  13 

1.7 

2.270 

2.297 

2.324 

2.351 

2.378 

2.405 

2.433 

2.461 

2.488 

2.516 

2.545 

3 

5    8  11  14 

1.8 

2.545 

2.573 

2.602 

2.630 

2.659 

2.688 

2.717 

2.746 

2.776 

2.806 

2.835 

3 

6    9  12  15 

1.9 

2.835 

2.865 

2.895 

2.926 

2.956 

2.986 

3.017 

3.048 

3.079 

3.110 

3.142 

3 

6    9  12  15 

2.0 

3.14 

3.17 

3.20 

3.24 

327 

330 

333 

337 

3.40 

3.43 

3.46 

0 

1112 

2.1 

3.46 

3.50 

3.53 

3.56 

3.60 

3.63 

3.66 

3.70 

3.73 

3.77 

3.80 

0 

1112 

22 

3.80 

3.84 

3.87 

3.91 

3.94 

3.98 

4.01 

4.05 

4.08 

4.12 

4.15 

0 

1112 

23 

4.15 

4.19 

423 

426 

430 

434 

437 

4.41 

4.45 

4.49 

4.52 

0 

1112 

2.4 

4.52 

4.56 

4.60 

4.64 

4.68 

4.71 

4.75 

4.79 

4.83 

4.87 

4.91 

0 

112    2 

2.5 

4.91 

4.95 

4.99 

5.03 

5.07 

5.11 

5.15 

5.19 

5.23 

527 

531 

0 

112    2 

2.6 

5.31 

5.35 

5.39 

5.43 

5.47 

5.52 

5.56 

5.60 

5.64 

5.68 

5.73 

0 

112    2 

2.7 

5.73 

5.77 

5.81 

5.85 

5.90 

5.94 

5.98 

6.03 

6.07 

6.11 

6.16 

0 

112    2 

2.8 

6.16 

6.20 

6.25 

6.29 

633 

638 

6.42 

6.47 

6.51 

6.56 

6.61 

0 

112    2 

2.9 

6.61 

6.65 

6.70 

6.74 

6.79 

6.83 

6.88 

6.93 

6.97 

7.02 

7.07 

0 

112    2 

3.0 

7.07 

7.12 

7.16 

721 

7.26 

7.31 

735 

7.40 

7.45 

7.50 

7.55 

0 

112    2 

3.1 

7.55 

7.60 

7.65 

7.69 

7.74 

7.79 

7.84 

7.89 

7.94 

7.99 

8.04 

0 

1-12    2 

3.2 

8.04 

8.09 

8.14 

8.19 

8.24 

830 

835 

8.40 

8.45 

8.50 

8.55 

1 

12    2    3 

3.3 

8.55 

8.60 

8.66 

8.71 

8.76 

8.81 

8.87 

8.92 

8.97 

9.03 

9.08 

1 

12    2    3 

3.4 

9.08 

9.13 

9.19 

924 

9.29 

935 

9.40 

9.46 

9.51 

9.57 

9.62 

1 

12    2    3 

3.5 

9.62 

9.68 

9.73 

9.79 

9.84 

9.90 

9.95 

10.01 

10.07 

10.12 

10.18 

1 

12    2    3 

3.6 

10.18 

10.24 

1029 

1035 

10.41 

10.46 

10.52 

10.58 

10.64 

10.69 

10.75 

1 

12    2    3 

3.7 

10.75 

10.81 

10.87 

10.93 

10.99 

11.04 

11.10 

11.16 

1122 

11.28 

11.34 

1 

12    2    3 

3.8 

11.34 

11.40 

11.46 

11.52 

11.58 

11.64 

11.70 

11.76 

11.82 

11.88 

11.95 

1 

12    2    3 

3.9 

11.95 

12.01 

12.07 

12.13 

12.19 

12.25 

.  12.32 

12.38 

12.44 

12.50 

12.57 

1 

12    2    3 

4.0 

12.57 

12.63 

12.69 

12.76 

12.82 

12.88 

12.95 

13.01 

13.07 

13.14 

13.20 

1 

12    3    3 

4.1 

1320 

1327 

1323 

13.40 

13.46 

13.53 

13.59 

13.66 

13.72 

13.79 

13.85 

1 

12    3   3 

4.2 

13.85 

13.92 

13.99 

14.05 

14.12 

14.19 

1425 

1432 

1439 

14.45 

14.52 

1 

12    3    3 

42 

14.52 

14.59 

14.66 

14.73 

14.79 

14.86 

14.93 

15.00 

15.07 

15.14 

15.21 

1 

12    3    3 

4.4 

15.21 

15.27 

1534 

15.41 

15.48 

15.55 

15.62 

15.69 

15.76 

15.83 

15.90 

1 

12    3    3 

4.5 

15.90 

15.98 

16.05 

16.12 

16.19 

16.26 

1633 

16.40 

16.47 

16.55 

16.62 

1 

12    3    4 

4.6 

16.62 

16.69 

16.76 

16.84 

16.91 

16.98 

17.06 

17.13 

17.20 

17.28 

17.35 

1 

12    3    4 

4.7 

17.35 

17.42 

17.50 

17.57 

17.65 

17.72 

17.80 

17.87 

17.95 

18.02 

18.10 

1 

12    3    4 

4.8 

18.10 

18.17 

18.25 

1832 

18.40 

18.47 

18.55 

18.63 

18.70 

18.78 

18.86 

1 

2    2    3    4 

4.9 

18.86 

18.93 

19.01 

19.09 

19.17 

1924 

1922 

19.40 

19.48 

19.56 

19.63 

1 

2    2    3    4 

5. 

19.6 

20.4 

21.2 

22.1 

22.9 

23.8 

24.6 

25.5 

26.4 

27.3 

283 

1 

2    3    3    4 

6. 

282 

29.2 

30.2 

31.2 

32.2 

332 

34.2 

35.3 

36.3 

37.4 

38.5 

1 

2    3    4    5 

7. 

38.5 

39.6 

40.7 

41.9 

43.0 

442 

45.4 

46.6 

47.8 

49.0 

503 

1 

2    4    5    6 

8. 

503 

51.5 

52.8 

54.1 

55.4 

56.7 

58.1 

59.4 

60.8 

62.2 

63.6 

1 

3    4    5    7 

9. 

63.6 

65.0 

66.5 

67.9 

69.4 

70.9 

72.4 

73.9 

75.4 

77.0 

78.5 

1 

3    4    6    7 

(6) 


(Moving  the  decimal  point  to  the  RIGHT  in  n 
is  equivalent  to  moving  it  to  the  LEFT  in  1  /n) 


Tenths  of  the 


Tabular  Differen 

1© 

9 

S 

1 

6 

S 

4 

3 

2 

a 

0 

n 

9. 

1    2 

3    4   5 

.1000 

.1010 

.1020 

.1031 

.1042 

.1053 

.1064 

.1075 

.1087 

.1099 

.1111 

1 

2 

3   4   6 

.1111 

.1124 

.1136 

.1149 

.1163 

.1176 

.1190 

.1205 

.1220 

.1235 

.1250 

go 

1 

3 

4    6    7 

.1250 

.1266 

.1282 

.1299 

.1316 

.1333 

.1351 

.1370 

.1389 

.1408 

.1429 

7. 

2 

4 

5    7   9 

.1429 

.1449 

.1471 

.1493 

.1515 

.1538 

2 

4 

7   9  11 

.1538 

.1562 

.1587 

.1613 

.1639 

.1667 

6. 

3 

5 

8  10  13 

.1667 

.1669 

.1672 

.1675 

.1678 

.1681 

.1684 

.1686 

.1689 

.1692 

.1695 

5.9 

0 

1 

111 

.1695 

.1698 

.1701 

.1704 

.1706 

.1709 

.1712 

.1715 

.1718 

.1721 

.1724 

5.8 

0 

1 

111 

.1724 

.1727 

.1730 

.1733 

.1736 

.1739 

.1742 

.1745 

.1748 

.1751 

.1754 

5.7 

0 

1 

112 

.1754 

.1757 

.1761 

.1764 

.1767 

.1770 

.1773 

.1776 

.1779 

.1783 

.1786 

5.6 

0 

1 

112 

.1786 

.1789 

.1792 

.1795 

.1799 

.1802 

.1805 

.1808 

.1812 

.1815 

.1818 

53 

0 

1 

112 

.1818 

.1821 

.1825 

.1828 

.1832 

.1835 

.1838 

.1842 

.1845 

.1848 

.1852 

5.4 

0 

1 

112 

.1852 

.1855 

.1859 

.1862 

.1866 

.1869 

.1873 

.1876 

.1880 

.1883 

.1887 

5.3 

0 

1 

112 

.1887 

.1890 

.1894 

.1898 

.1901 

.1905 

.1908 

.1912 

.1916 

.1919 

.1923 

52 

0 

1 

112 

.1923 

.1927 

.1931 

.1934 

.1938 

.1942 

.1946 

.1949 

.1953 

.1957 

.1961 

5.1 

0 

1 

12    2 

.1961 

.1965 

.1969 

.1972 

.1976 

.1980 

.1984 

.1988 

.1992 

.1996 

2000 

5.0 

0 

1 

12    2 

.2000 

2004 

.2008 

2012 

2016 

2020 

2024 

2028 

2033 

2037 

2041 

4.9 

0 

1 

12    2 

2041 

2045 

2049 

.2053 

2058 

2062 

2066 

2070 

2075 

2079 

2083 

4.8 

0 

1 

12    2 

2083 

2088 

2092 

2096 

2101 

2105 

2110 

2114 

2119 

2123 

2128 

4.7 

0 

1 

12    2 

2128 

2132 

2137 

2141 

2146 

2151 

2155 

2160 

2165 

2169 

2174 

4.6 

0 

1 

12    2 

2174 

2179 

2183 

2188 

2193 

2198 

2203 

2208 

2212 

2217 

.2222 

43 

0 

1 

12    2 

2222 

2227 

2232 

2237 

.2242 

2247 

2252 

2257 

2262 

2268 

2273 

4.4 

1 

1 

2    2    3 

2273 

2278 

2283 

2288 

2294 

2299 

2304 

2309 

2315 

2320 

2326 

43 

1 

1 

2    2    3 

2326 

2331 

2336 

2342 

2347 

.2353 

2358 

2364 

2370 

2375 

2381 

42 

1 

1 

2    2    3 

.2381 

.2387 

2392 

.2398 

2404 

2410 

2415 

2421 

2427 

2433 

2439 

4.1 

1 

1 

2    2    3 

2439 

2445 

2451 

2457 

2463 

2469 

2475 

2481 

2488 

2494 

2500 

4.0 

1 

1 

2    2    3 

2500 

2506 

.2513 

2519 

2525 

2532 

2538 

2545 

2551 

2558 

2564 

3.9 

1 

1 

2    3    3 

2564 

2571 

2577 

2584 

2591 

2597 

2604 

2611 

2618 

2625 

2632 

3.8 

1 

1 

2    3    3 

2632 

2639 

2646 

2653 

2660 

2667 

2674 

2681 

2688 

2695 

2703 

3.7 

1 

1 

2    3    4 

2703 

2710 

2717 

2725 

2732 

2740 

2747 

2755 

2762 

2770 

2778 

3.6 

1 

2 

2    3    4 

2778 

2786 

2793 

2801 

2809 

2817 

2825 

2833 

2841 

.2849 

2857 

33 

1 

2 

2    3    4 

2857 

2865 

2874 

2882 

2890 

2899 

2907 

2915 

2924 

2933 

2941 

3.4 

1 

2 

3    3    4 

2941 

2950 

2959 

2967 

2976 

2985 

2994 

3003 

3012 

3021 

3030 

33 

1 

2 

3    4    4 

3030 

3040 

3049 

3058 

3067 

3077 

3086 

3096 

3106 

3115 

3125 

32 

1 

2 

3    4    5 

.3125 

3135 

3145 

3155 

3165 

3175 

3185 

3195 

3205 

3215 

3226 

3.1 

1 

2 

3    4    5 

3226 

3236 

3247 

3257 

3268 

3279 

3289 

3300 

3311 

3322 

3333 

3.0 

1 

2 

3    4   5 

.333 

334 

336 

337 

338 

339 

340 

341 

342 

344 

345 

2.9 

0 

0 

0    0    1 

345 

346 

347 

348 

350 

351 

352 

353 

355 

356 

357 

2.8 

0 

0 

0    0    1 

357 

358 

360 

361 

362 

364 

365 

366 

368 

369 

370 

2.7 

0 

0 

Oil 

370 

372 

373 

375 

376 

377 

379 

380 

382 

383 

385 

2.6 

0 

0 

Oil 

385 

386 

388 

389 

391 

392 

394 

395 

397 

398 

.400 

2.5 

0 

0 

Oil 

.400 

.402 

.403 

.405 

.407 

.408 

.410 

.412 

.413 

.415 

.417 

2.4 

0 

0 

Oil 

.417 

.418 

.420 

.422 

.424 

.426 

.427 

.429 

.431 

.433 

.435 

23 

0 

0 

111 

.435 

.437 

.439 

.441 

.442 

.444 

.446 

.448 

.450 

.452 

.455 

22 

0 

0 

111 

.455 

.457 

.459 

.461 

.463 

.465 

.467 

.469 

.472 

.474 

.476 

2.1 

0 

0 

111 

.476 

.478 

.481 

.483 

.485 

.488 

.490 

.493 

.495 

.498 

.500 

2.0 

0 

0 

111 

.500 

.503 

.505 

.508 

310 

.513 

.515 

.518 

.521 

.524 

.526 

1.9 

0 

1 

111 

.526 

.529 

.532 

.535 

.538 

.541 

.543 

.546 

.549 

.552 

.556 

1.8 

0 

1 

111 

.556 

.559 

.562 

.565 

.568 

.571 

.575 

.578 

.581 

.585 

.588 

1.7 

0 

1 

112 

.588 

.592 

.595 

.599 

.602 

.606 

.610 

.613 

.617 

.621 

.625 

1.6 

0 

1 

112 

.625 

.629 

.633 

.637 

.641 

.645 

.649 

.654 

.658 

.662 

.667 

1.5 

0 

1 

12    2 

.667 

.671 

.676 

.680 

.685 

.690 

.694 

.699 

.704 

.709 

.714 

1.4 

0 

1 

12    2 

.714 

.719 

.725 

.730 

.735 

.741 

.746 

.752 

.758 

.763 

.769 

13 

1 

1 

2    2    3 

.769 

.775 

.781 

.787 

.794 

.800 

.806 

.813 

.820 

.826 

.833 

1.2 

1 

1 

2    3    3 

.833 

.840 

.847 

.855 

.862 

.870 

.877 

.885 

.893 

.901 

.909   . 

1.1 

1 

2 

2    3    4 

.909 

.917 

.926 

.935 

.943 

.952 

.962 

.971 

.980 

.990 

1.0 

1 

2 

3    4   5 

# 


in 


r.O5 


1/tt  =  031831 


(7) 


1/^  =  0.10132 


*& 


Sine 


#5 


'5 

o5 


JO 

L    Jl> 

.1 

2 

3 

JS 

.4 

M 
5 

.4 

.6 

~1T^ 

.8  l 

B 

s>@>° 

Ta 
1 

Tenths  of  the 

ular  Difference 

2  3  4  5 

0.000000 

0° 

0.000000 

001745  003491  005238  006981 

008727 

010472  012217  013962  015707 

017452 

89 

175349524698873 

1 

01745 

01920 

02094 

02269 

02443 

02618 

02792 

02967 

03141 

03316 

03490 

88 

17 

35  52  70  87 

2 

03490 

03664 

03839 

04013 

04188 

04362 

04536 

04711 

04835 

05059 

05234 

87 

17 

35  52  70  87 

3 

05234 

05408 

05582 

05756 

05931 

06105 

06279 

06453 

06627 

06802 

06976 

86 

17 

35  52  70  87 

4 

06976 

07150 

07324 

07498 

07672 

07846 

08020 

08194 

08368 

08542 

08716 

85 

17 

35  52  70  87 

5 

03716 

08889 

09063 

09237 

09411 

09585 

09758 

09932 

10106 

10279 

10453 

84 

17 

35  52  69  87 

6 

10453 

10626 

10800 

10973 

11147 

11320 

11494 

11667 

11840 

12014 

12187 

83 

17 

35  52  69  87 

7 

12187 

12360 

12533 

12706 

12880 

13053 

13226 

13399 

13572 

13744 

13917 

82 

17 

35  52  69  87 

8 

13917 

14090 

14263 

14436 

14608 

14781 

14954 

15126 

15299 

15471 

15643 

81 

17 

35  52  69  86 

9 

15643 

15816 

15988 

16160 

16333 

16505 

16677 

16849 

17021 

17193 

0.17365 

80° 

17 

34  52  69  86 

10° 

0.1736 

1754 

1771 

1788 

1805 

1822 

1840 

1857 

1874 

1891 

1908 

79 

2 

3    5    7    9 

11 

1908 

1925 

1942 

1959 

1977 

1994 

2011 

2028 

2045 

2062 

2079 

78 

2 

3    5    7    9 

12 

2079 

2096 

2113 

2130 

2147 

2164 

2181 

2198 

2215 

2233 

2250 

77 

2 

3    5    7    9 

13 

2250 

2267 

2284 

2300 

2317 

2334 

2351 

2368 

2385 

2402 

2419 

76 

2 

3    5    7    8 

14 

2419 

2436 

2453 

2470 

2487 

2504 

2521 

2538 

2554 

2571 

2588 

75 

2 

3    5    7    8 

15 

2588 

2605 

2622 

2639 

2656 

2672 

2689 

2706 

2723 

2740 

2756 

74 

2 

3    5    7    8 

16 

2756 

2773 

2790 

2807 

2823 

2840 

2857 

2874 

2890 

2907 

2924 

73 

2 

3    5    7    8 

17 

2924 

2940 

2957 

2974 

2990 

3007 

3024 

3040 

3057 

3074 

3090 

72 

2 

3    5    7    8 

18 

3090 

3107 

3123 

3140 

3156 

3173 

3190 

3206 

3223 

3239 

3256 

71 

2 

3    5    7    8 

19 

3256 

3272 

3289 

3305 

3322 

3338 

3355 

3371 

3387 

3404 

0.3420 

7Q° 

2 

3    5    7    8 

20° 

0.3420 

3437 

3453 

3469 

3486 

3502 

3518 

3535 

3551 

3567 

3584 

69 

2 

3    5    7    8 

21 

3584 

3600 

3616 

3633 

3649 

3665 

3681 

3697 

3714 

3730 

3746 

68 

2 

3    5    6    8 

22 

3746 

3762 

3778 

3795 

3811 

3827 

3843 

3859 

3875 

3891 

3907 

67 

2 

3    5    6    8 

23 

3907 

3923 

3939 

3955 

3971 

3987 

4003 

4019 

4035 

4051 

4067 

66 

2 

3    5    6    8 

24 

4067 

4083 

4099 

4115 

4131 

4147 

4163 

4179 

4195 

4210 

4226 

65 

2 

3    5    6    8 

25 

4226 

4242 

4258 

4274 

4289 

4305 

4321 

4337 

4352 

4368 

4384 

64 

2 

3    5    6    8 

26 

4384 

4399 

4415 

4431 

4446 

4462 

4478 

4493 

4509 

4524 

4540 

63 

2 

3    5    6    8 

27 

4540 

4555 

4571 

4586 

4602 

4617 

4633 

4648 

4664 

4679 

4695 

62 

2 

3    5    6    8 

28 

4695 

4710 

4726 

4741 

4756 

4772 

4787 

4802 

4818 

4833 

4848 

61 

2 

3    5    6    8 

29 

4848 

4863 

4879 

4894 

4909 

4924 

4939 

4955 

4970 

4985 

0.5000 

(S0° 

2 

3    5    6    8 

30° 

0.5000 

5015 

5030 

5045 

5060 

5075 

5090 

5105 

5120 

5135 

5150 

59 

2 

3    5    6    8 

31 

5150 

5165 

5180 

5195 

5210 

5225 

5240 

5255 

5270 

5284 

5299 

58 

1 

3    4    6   7 

32 

5299 

5314 

5329 

5344 

5358 

5373 

5388 

5402 

5417 

5432 

5446 

57 

1 

3    4    6   7 

33 

5446 

5461 

5476 

5490 

5505 

5519 

5534 

5548 

5563 

5577 

5592 

56 

1 

3    4    6   7 

34 

5592 

5606 

5621 

5635 

5650 

5664 

5678 

5693 

5707 

5721 

5736 

55 

1 

3    4    6    7 

35 

5736 

5750 

5764 

5779 

5793 

5807 

5821 

5835 

5850 

5864 

5878 

54 

1 

3    4    6    7 

36 

5878 

5892 

5906 

5920 

5934 

5948 

5962 

5976 

5990 

6004 

6018 

53 

1 

3    4    6   7 

37 

.6018 

6032 

6046 

6060 

6074 

6088 

6101 

6115 

6129 

6143 

6157 

52 

1 

3    4    6    7 

38 

6157 

6170 

6184 

6198 

6211 

6225 

6239 

6252 

6266 

6280 

6293 

51 

1 

3    4    5    7 

39 

6293 

6307 

6320 

6334 

6347 

6361 

6374 

6388 

6401 

6414 

0.6428 

B0° 

1 

3    4    5    7 

40° 

0.6428 

6441 

6455 

6468 

6481 

6494 

6508 

6521 

6534 

6547 

6561 

49 

1 

3    4    5    7 

41 

6561 

6574 

6587 

6600 

6613 

6626 

6639 

6652 

6665 

6678 

6691 

48 

1 

3    4    5    7 

42 

6691 

6704 

6717 

6730 

6743 

6756 

6769 

678? 

6794 

6807 

6820 

47 

1 

3    4    5    6 

43 

6820 

6833 

6845 

6858 

6871 

6884 

6896 

6909 

6921 

6934 

6947 

46 

1 

3    4    5    6 

44 

6947 

6959 

6972 

6984 

6997 

7009 

7022 

7034 

7046 

7059' 

0.7071 

4S° 

1 

2    4    5    6 

45° 

0.7071 

(8) 


Sine 


.0 

.1    2  3  .4 

M 

•4  J  2  1- 

JG> 

Tenths  of  the 
Tabular  Difference 

.5 

j6  .7  A      j>1 

4§° 

12  3  4  5 

0.7071 

45° 

0.7071 

7083  7096  7108  7120 

7133 

7145  7157  7169  7181 

7193 

44 

12  4  5  6 

46 

7193 

7206  7218  7230  7242 

7254 

7266  7278  7290  7302 

7314 

43 

12  4  5  6 

47 

7314 

7325  7337  7349  7361 

7373 

7385  7396  7408  7420 

7431 

42 

12  4  5  6 

48 

7431 

7443  7455  7466  7478 

7490 

7501  7513  7524  7536 

7547 

41 

12  3  5  6 

49 

7547 

7559  7570  7581  7593 

7604 

7615  7627  7638  7649 

7660 

40° 

12  3  5  6 

50° 

0.7660 

7672  7683  7694  7705 

7716 

7727  7738  7749  7760  0.7771 

39 

12  3  4  6 

51 

7771 

7782  7793  7804  7815 

7826 

7837  7848  7859  7869 

7880 

38 

12  3  4  5 

52 

7880 

7891  7902  7912  7923 

7934 

7944  7955  7965  7976 

7986 

37 

12  3  4  5 

53 

7986 

7997  8007  8018  8028 

8039 

8049  8059  8070  8080 

8090 

36 

12  3  4  5 

54 

8090 

8100  8111  8121  8131 

8141 

8151  8161  8171  8181 

8192 

35 

12  3  4  5 

55 

8192 

8202  8211  8221  8231 

8241 

8251  8261  8271  8281 

8290 

34 

12  3  4  5 

56 

8290 

8300  8310  8320  8329 

8339 

8348  8358  8368  8377 

8387 

33 

12  3  4  5 

57 

8387 

8396  8406  8415  8425 

8434 

8443  8453  8462  8471 

8480 

32 

12  3  4  5 

58 

8480 

8490  8499  8508  8517 

8526 

8536  8545  8554  8563 

8572 

31 

12  3  4  5 

59 

8572 

8581  8590  8599  8607 

8616 

8625  8634  8643  8652  0.8660 

30° 

12  3  4  4 

60° 

0.8660 

8669  8678  8686  8695 

8704 

8712  8721  8729  8738 

8746 

29 

12  3  3  4 

61 

8746 

8755  8763  8771  8780 

8788 

8796  8805  8813  8821 

8829 

28 

12  2  3  4 

62 

8829 

8838  8846  8854  8862 

8870 

8878  8886  8894  8902 

8910 

27 

12  2  3  4 

63 

8910 

8918  8926  8934  8942 

8949 

8957  8965  8973  8980 

8988 

26 

12  2  3  4 

64 

8988 

8996  9003  9011  9018 

9026 

9033  9041  9048  9056 

9063 

25 

12  2  3  4 

65 

9063 

9070  9078  9085  9092 

9100 

9107  9114  9121  9128 

9135 

24 

112  3  4 

66 

9135 

9143  9150  9157  9164 

9171 

9178  9184  9191  9198 

9205 

23 

112  3  3 

67 

9205 

9212  9219  9225  9232 

9239 

9245  9252  9259  9265 

9272 

22 

112  3  3 

68 

9272 

9278  9285  9291  9298 

9304 

9311  9317  9323  9330 

9336 

21 

112  3  3 

69 

9336 

9342  9348  9354  9361 

9367 

9373  9379  9385  9391  0.9397 

2©° 

112  2  3 

70° 

0.9397 

9403  9409  9415  9421 

9426 

9432  9438  9444  9449 

9455 

19 

112  2  3 

71 

9455 

9461  9466  9472  9478 

9483 

9489  9494  9500  9505 

9511 

18 

112  2  3 

72 

9511 

9516  9521  9527  9532 

9537 

9542  9548  9553  9558 

9563 

17 

112  2  3 

73 

9563 

9568  9573  9578  9583 

9588 

9593  9598  9603  9608 

9613 

16 

0  112  2 

74 

9613 

9617  9622  9627  9632 

9636 

9641  9646  9650  9655 

9659 

15 

0  112  2 

75 

9659 

9664  9668  9673  9677 

9681 

9686  9690  9694  9699 

9703 

14 

0  112  2 

76 

9703 

9707  9711  9715  9720 

9724 

9728  9732  9736  9740 

9744 

13 

0  112  2 

77 

9744 

9748  9751  9755  9759 

9763 

9767  9770  9774  9778 

9781 

12 

0  112  2 

78 

9781 

9785  9789  9792  9796 

9799 

9803  9806  9810  9813 

9816 

.  11 

0  1112 

79 

9816 

9820  9823  9826  9829 

9833 

9836  9839  9842  9845 

0.9848 

10° 

0  1112 

80° 

0.9848 

9851  9854  9857  9860 

9863 

9866  9869  9871  9874 

9877 

9 

0  1111 

81 

9877 

9880  9882  9885  9888 

9890 

9893  9895  9898  9900 

9903 

8 

0  1111 

82 

9903 

9905  9907  9910  9912 

9914 

9917  .9919  9921  9923 

9925 

7 

0  0  111 

83 

9925 

9928  9930  9932  9934 

9936 

9938  9940  9942  9943 

9945 

6 

0  0  111 

84 

9945 

9947  9949  9951  9952 

9954 

9956  9957  9959  9960 

9962 

5 

0  0  111 

85 

9962 

9963  9965  9966  9968 

9969 

9971  9972  9973  9974 

9976 

4 

0  0  0  11 

86 

9976 

9977  9978  9979  9980 

9981 

9982  9983  9984  9985 

9986 

3 

0  0  0  0  1 

87 

9986 

9987  9988  9989  9990 

9990 

9991  9992  9993  9993 

9994 

2 

0  0  0  0  0 

88 

9994 

9995  9995  9996  9996 

9997 

9997  9997  9998  9998 

0.9998 

1 

0  0  0  0  0 

89 

0.9998 

9999  9999  9999  9999 

J  0000 

0000  0000  0000  0000 

1.0000 

©° 

0  0  0  0  0 

90° 

1.0000 

(9) 


M 


Tangent 


Coft&mgeimft 


0 

.1  2 

-T    M 

M 

.4 

J 

Ja 

1  B 

.9    1 

3    A 

5 

* 

.7 

""X" 

90° 

0.000000 

0° 

0.000000 

001745  003491  005236  006981 

008727 

010472 

012218  013964  015709     017455 

89 

1 

01748 

01920    02095 

02269    02444 

02619 

02793 

02968 

03143 

03317       03492 

88 

2 

03492 

03667    03842 

04016    04191 

04366 

04541 

04716 

04891 

05066       05241 

87 

3 

05241 

05416    05591 

05766    05941 

06116 

06291 

06467 

06642 

06817       06993 

86 

4 

06993 

07168    07344 

07519    07695 

07870 

08046 

08221 

08397 

08573       08749 

85 

5 

08749 

08925    09101 

09277    09453 

09629 

09805 

09981 

10158 

10334      10510 

84 

6 

10510 

10687    10863 

11040    11217 

11394 

11570 

11747 

11924 

12101       12278 

83 

7 

12278 

12456    12633 

12810    12988 

13165 

13343 

13521 

13698 

13876       14054 

82 

8 

14054 

14232    14410 

14588    14767 

14945 

15124 

15302 

15481 

15660       15838 

81 

9 

15838 

16017    16196 

16376    16555 

16734 

16914 

17093 

17273 

17453    0.17633 

so° 

10° 

0.1763 

1781    1799 

1817    1835 

1853 

1871 

1890 

1908 

1926      1944 

79 

11 

1944 

1962    1980 

1998    2016 

2035 

2053 

2071 

2089 

2107      2126 

78 

12 

2126 

2144   2162 

2180    2199 

2217 

2235 

2254 

2272 

2290      2309 

77 

13 

2309 

2327   2345 

2364    2382 

2401 

2419 

2438 

2456 

2475      2493 

76 

14 

2493 

2512    2530 

2549    2568 

2586 

2605 

2623 

2642 

2661      2679 

75 

IS 

2679 

2698   2717 

2736   2754 

2773 

2792 

2811 

2830 

2849      2867 

74 

16 

2867 

2886    2905 

2924    2943 

2962 

2981 

3000 

3019 

3038      3057 

73 

17 

3057 

3076   3096 

3115    3134 

3153 

3172 

3191 

3211 

3230      3249 

72 

18 

3249 

3269    3288 

3307   3327 

3346 

3365 

3385 

3404 

3424      3443 

71 

19 

3443 

3463   3482 

3502   3522 

3541 

3561 

3581 

3600 

3620  0.3640 

7©° 

30° 

0.3640 

3659   3679 

3699   3719 

3739 

3759 

3779 

3799 

3819      3839 

69 

21 

3839 

3859    3879 

3899    3919 

3939 

3959 

3979 

4000 

4020      4040 

68 

22 

4040 

4061    4081 

4101    4122 

4142 

4163 

4183 

4204 

4224      4245 

67 

23 

4245 

4265    4286 

4307    4327 

4348 

4369 

4390 

4411 

4431      4452 

66 

24 

4452 

4473   4494 

4515   4536 

4557 

4578 

4599 

4621 

4642      4663 

65 

25 

4663 

4684   4706 

4727   4748 

4770 

4791 

4813 

4834 

4856      4877 

64 

26 

4877 

4899    4921 

4942    4964 

4986 

5008 

5029 

5051 

5073      5095 

63 

27 

5095 

5117    5139 

5161    5184 

5206 

5228 

5250 

5272 

5295      5317 

62 

28 

5317 

5340    5362 

5384   5407 

5430 

5452 

5475 

5498 

5520      5543 

61 

29 

5543 

5566   5589 

5612   5635 

5658 

5681 

5704 

5727 

5750  0.5774 

(SO0 

30° 

0.5774 

5797    5820 

5844   5867 

5890 

5914 

5938 

5961 

5985      6009 

59 

31 

6009 

6032    6056 

6080   6104 

6128 

6152 

6176 

6200 

6224      6249 

58 

32 

6249 

6273    6297 

6322   6346 

6371 

6395 

6420 

6445 

6469      6494 

57 

33 

6494 

6519   6544 

6569   6594 

6619 

6644 

6669 

6694 

6720      6745 

56 

34 

6745 

6771   6796 

6822   6847 

6873 

6899 

6924 

6950 

6976      7002 

55 

35 

7002 

7028   7054 

7080   7107 

7133 

7159 

7186 

7212 

7239      7265 

54 

36 

7265 

7292    7319 

7346   7373 

7400 

7427 

7454 

7481 

7508      7536 

53 

37 

7536 

7563   7590 

7618   7646 

7673 

7701 

7729 

7757 

7785      7813 

52 

38 

7813 

7841    7869 

7898    7926 

7954 

7983 

8012 

8040 

8069      8098 

51 

39 

8098 

8127   8156 

8185    8214 

8243 

8273 

8302 

8332 

8361  0.8391 

s©° 

40° 

0.8391 

8421   8451 

8481   8511 

8541 

8571 

8601 

8632 

8662      8693 

49 

41 

8693 

8724   8754 

8785    8816 

8847 

8878 

8910 

8941 

8972      9004 

48 

42 

9004 

9036   9067 

9099   9131 

9163 

9195 

9228 

9260 

9293      9325 

47 

43 

9325 

9358   9391 

9424   9457 

9490 

9523 

9556 

9590 

9623  0.9657 

46 

44 

0.9657 

9691   9725 

9759   9793 

9827 

9861 

9896 

9930 

9965jl,0000 

4S° 

45° 

1.0000 

Tenths  of  the 

Tabular  Difference 

12   3  4  5 


175  349524698873 

17  35  52  70  87 

17  35  52  70  87 

18  35  53  70  88 
18  35  53  70  88 

18  35  53  70  88 

18  35  53  71  88 

18  36  53  71  89 

18  36  54  71  89 

18  36  54  72  90 

2    4  5    7    9 

2    4  5    7   9 

2    4  579 

2    4  6    7   9 

2    4  6    7    9 

2    4  6    8    9 

2    4  6    8   9 

2    4  6    810 

2    4  6    810 

2    4  6    810 

2    4  6    810 

2    4  6    8  10 

2    4  6    810 

2    4  6    810 

2    4  6    811 

2    4  6   911 

2    4  7    911 

2    4  7    911 

2    5  7    911 

2    5  7    912 

2    5  7    912 

2    5  7  1012 

2  5  71012 

3  5  8  1013 
3    5  81013 

3    5  81113 

3    5  8  1114 

3    6  8  1114 

3    6  91114 

3    6  9  12  15 


6   9  12  15 
6    9  12  16 

6  10  13  16 

7  10  13  17 
7  10  14  17 


(10) 


Tangent 


.0 

L.   & 

.© 

.7 

J8 

.4 

J5 

i 

.6 

M 

2 

.1 

B 

45° 

Tenths  of  the 

.1 

2 

.3 

Tabular  Difference 

.7 

.8 

~  .9   1 

12   3  4   5 

1.0000 

45° 

1.0000 

0035 

0070 

0105 

0141 

0176 

0212 

0247 

0283 

0319 

0355 

44 

4    7  11  14  18 

46 

0355 

0392 

0428 

0464 

0501 

0538 

0575 

0612 

0649 

0686 

0724 

43 

4    7  11  15  18 

47 

0724 

0761 

0799 

0837 

0875 

0913 

0951 

0990 

1028 

1067 

1106 

42 

4    8  11 15  19 

48 

1106 

1145 

1184 

1224 

1263 

1303 

1343 

1383 

1423 

1463 

1504 

41 

4    8  12  16  20 

49 

1504 

1544 

1585 

1626 

1667 

1708 

1750 

1792 

1833 

1875 

1.1918 

m° 

4    8  12  17  21 

50° 

1.1918 

1960 

2002 

2045 

2088 

2131 

2174 

2218 

2261 

2305 

2349 

39 

4    9  13  17  22 

'  51 

2349 

2393 

2437 

2482 

2527 

2572 

2617 

2662 

2708 

2753 

2799 

38 

5    91418  23 

52 

2799 

2846 

2892 

2938 

2985 

3032 

3079 

3127 

3175 

3222 

3270 

37 

5    9  14  19  24 

53 

3270 

3319 

3367 

3416 

3465 

3514 

3564 

3613 

3663 

3713 

3764 

36 

5  10  15  20  25 

54 

3764 

3814 

3865 

3916 

3968 

4019 

4071 

4124 

4176 

4229 

1.4281 

35 

5  10  16  2126 

55 

1.4281 

4335 

4388 

4442 

4496 

4550 

4605 

4659 

4715 

4770 

4826 

34 

5  11  16  22  27 

56 

4826 

4882 

4938 

4994 

5051 

5108 

5166 

5224 

5282 

5340 

5399 

33 

6  11  17  23  29 

57 

5399 

5458 

5517 

5577 

5637 

5697 

5757 

5818 

5880 

5941 

6003 

32 

6  12  18  24  30 

58 

6003 

6066 

6128 

6191 

6255 

6319 

6383 

6447 

6512 

6577 

6643 

31 

6  13  19  26  32 

59 

60° 

1.6643 

6709 

6775 

6842 

6909 

6977 

7045 

7113 

7182 

7251 

1.7321 

30° 

29 

7  14  20  27  34 

1.732 

1.739 

1.746 

1.753 

1.760 

1.767 

1.775 

1.782 

1.789 

1.797 

1.804 

112    3    4 

61 

1.804 

1.811 

1.819 

1.827 

1.834 

1.842 

1.849 

1.857 

1.865 

1.873 

1.881 

28 

12    2   3   4 

62 

1.881 

1.889 

1.897 

1.905 

1.913 

1.921 

1.929 

1.937 

1.946 

1.954 

1.963 

27 

12    2    3    4 

63 

1.963 

1.971 

1.980 

1.988 

1.997 

2.006 

2.014 

2.023 

2.032 

2.041 

2.050 

26 

12    3    4   4 

64 

2.050 

2.059 

2.069 

2.078 

2.087 

2.097 

2.106 

2.116 

2.125 

2.135 

2.145 

25 

12    3   4   5 

65 

2.145 

2.154 

2.164 

2.174 

2.184 

2.194 

2.204 

2.215 

2.225 

2.236 

2.246 

24 

12    3    4    5 

66 

2.246 

2.257 

2.267 

2.278 

2.289 

2.300 

2.311 

2.322 

2.333 

2.344 

2.356 

23 

12    3    4    5 

67 

2.356 

2.367 

2.379 

2.391 

2.402 

2.414 

2.426 

2.438 

2.450 

2.463 

2.475 

22 

12    4    5    6 

68 

2.475 

2.488 

2.500 

2.513 

2.526 

2.539 

2.552 

2.565 

2.578 

2.592 

2.605 

21 

13    4    5    7 

69 

2.605 

2.619 

2.633 

2.646 

2.660 

2.675 

2.689 

2.703 

2.718 

2.733 

2.747 

20° 

13    4   6    7 

70° 

2.747 

2.762 

2.778 

2.793 

2.808 

2.824 

2.840 

2.856 

2.872 

2.888 

2.904 

19 

2    3    5    6    8 

71 

2.904 

2.921 

2.937 

2.954 

2.971 

2.989 

3.006 

3.024 

3.042 

3.060 

3.078 

18 

2    3    5    7    9 

72 

3.078 

3.096 

3.115 

3.133 

3.152 

3.172 

3.191 

3.211 

3.230 

3.251 

3.271 

17 

2    4   6    8  10 

73 

3.271 

3.291 

3.312 

3.333 

3.354 

3.376 

3.398 

3.420 

3.442 

3.465 

3.487 

16 

2    4   6    9  11 

74 

3.487 

3.511 

3.534 

3.558 

3.582 

3.606 

3.630 

3.655 

3.681 

3.706 

3.732 

15 

2    5    7  10  12 

75 

3.732 

3.758 

3.785 

3.812 

3.839 

3.867 

3.895 

3.923 

3.952 

3.981 

4.011 

14 

3    6    8  11  14 

76 
77 

4.011 
4.331 

4.041 
4.366 

4.071 
4.402 

4.102 
4.437 

4.134 
4.474 

4.165 
4.511 

4.198 
4.548 

4.230 
4.586 

4.264 
4.625 

4.297 
4.665 

4.331 
4.705 

13 
12 

3    6  10  13  16 

co      35-^K) 

78 

4.705 

4.745 

4.787 

4.829 

4.872 

4.915 

4.959 

5.005 

5.050 

5.097 

5.145 

11 

1     40-^8 

79 

5.145 

5.193 

5.242 

5.292 

5.343 

5.396 

5.449 

5.503 

5.558 

5.614 

5.671 

10° 

1     48~ S7 

80° 

5.671 

5.730 

5.789 

5.850 

5.912 

5.976 

6.041 

6.107 

6.174 

6.243 

6.314 

9 

f!     59—71 

81 

6.314 

6.386 

6.460 

6.535 

6.612 

6.691 

6.772 

6.855 

6.940 

7.026 

7.115 

8 

Z     72—89 

82 

7.115 

7.207 

7.300 

7.396 

7.495 

7.596 

7.700 

7.806 

7.916 

8.028 

8.144 

7 

=     92-116 

83 
84 

8.144 
9.514 

8.264 
9.677 

8.386 

9.845 

8.513 
10.019 

8.643 
10.199 

8.777 
10.385 

8.915 
10.579 

9.058 
10.780 

9.205 
10.988 

9.357 
11.205 

9.514 
11.430 

6 
S 

"   120—157 

Interpolation 

85 

11.430 

11.664 

11.909 

12.163 

12.429 

12.706 

12.996 

13.300 

13.617 

13.951 

14.301 

4 

accurate,  except 

86 
87 

14.301 
19.08 

14.669 
19.74 

15.056 
20.45 

15.464 
21.20 

15.895 
22.02 

16.350 
22.90 

16.832 
23.86 

17.343 

24.90 

17.886 
26.03 

18.464 

27.27 

19.081 
28.64 

3 

2 

the  lasl  figure 

Interpolation 
not  accurate 

88 

28.64 

30.14 

31.82 

33.69 

35.80 

38.19 

40.92 

44.07 

47.74 

52.08 

57.29 

1 

89 

57.29 

63.66 

71.62 

81.85 

95.49 

114.59 

143.24 

191.0 

286.5 

573.0 

00 

0° 

90° 

00 

(11) 


^ 


< 


W 


t*c 


* 


4/fo 

go"5 


Secant 


.0 

I.  .© 

.1 

2 

_J  jfi 

J> 

.6 

"IT" 

.1 

.© 

B@° 

1 
Tat 
1 

entt 

ular 

2 

s  of  the 
Difference 

3  4  5 

.3  .4 

"IT 

1.0000 

0° 

1.0000 

0000 

0000 

0000  0000 

0000 

0001 

0001 

0001 

0001 

0002 

89 

0 

0 

0  0  0 

1 

0002 

0002 

0002 

0003  0003 

0003 

0004 

0004 

0005 

0006 

0006 

88 

0 

0 

0  0  0 

2 

0006 

0007 

0007 

0008  0009 

0010 

0010 

0011 

0012 

0013 

0014 

87 

0 

0 

0  0  0 

3 

0014 

0015 

0016 

0017  0018 

0019 

0020 

0021 

0022 

0023 

0024 

86 

0 

0 

0  0  1 

4 

0024 

0026 

0027 

0028  0030 

0031 

0032 

0034 

0035 

0037 

0038 

85 

0 

0 

Oil 

5 

0038 

0040 

0041 

0043  0045 

0046 

0048 

0050 

0051 

0053 

0055 

84 

0 

0 

111 

6 

0055 

0057 

0059 

0061  0063 

0065 

0067 

0069 

0071 

0073 

0075 

83 

0 

0 

111 

7 

0075 

0077 

0079 

0082  0084 

0086 

0089 

0091 

0093 

0096 

0098 

82 

0 

0 

111 

8 

0098 

0101 

0103 

0106  0108 

0111 

0114 

0116 

0119 

0122 

0125 

81 

0 

1 

111 

9 

0125 

0127 

0130 

0133  0136 

0139 

0142 

0145 

0148 

0151 

1.0154 

BO° 

0 

1 

111 

10° 

1.0154 

0157 

0161 

0164  0167 

0170 

0174 

0177 

0180 

0184 

0187 

79 

0 

1 

112 

11 

0187 

0191 

0194 

0198  0201 

0205 

0209 

0212 

0216 

0220 

0223 

78 

0 

1 

112 

12 

0223 

0227 

0231 

0235  0239 

0243 

0247 

0251 

0255 

0259 

0263 

77 

0 

1 

12  2 

13 

0263 

0267 

0271 

0276  0280 

0284 

0288 

0293 

0297 

0302 

0306 

76 

0 

1 

12  2 

14 

0306 

0311 

0315 

0320  0324 

0329 

0334 

0338 

0343 

0348 

0353 

75 

1 

1 

12  2 

15 

0353 

0358 

0363 

0367  0372 

0377 

0382 

0388 

0393 

0398 

0403 

74 

1 

1 

2  2  3 

16 

0403 

0408 

0413 

0419  0424 

0429 

0435 

0440 

0446 

0451 

0457 

73 

1 

1 

2  2  3 

17 

0457 

0463 

0468 

0474  0480 

0485 

0491 

0497 

0503 

0509 

0515 

.  72 

1 

1 

2  2  3 

18 

0515 

0521 

0527 

0533  0539 

0545 

0551 

0557 

0564 

0570 

0576 

71 

1 

1 

2  2  3 

19 

0576 

0583 

0589 

0595  0602 

0608 

0615 

0622 

0628 

0635 

1.0642 

7(0° 

1 

1 

2  3  3 

20° 

1.0642 

0649 

0655 

0662  0669 

0676 

0683 

0690 

0697 

0704 

0711 

69 

1 

1 

2  3  3 

21 

0711 

0719 

0726 

0733  0740 

0748 

0755 

0763 

0770 

0778 

0785 

68 

1 

1 

2  3  4 

22 

0785 

0793 

0801 

0808  0816 

0824 

0832 

0840 

0848 

0856 

0864 

67 

1 

2 

2  3  4 

23 

0864 

0872 

0880 

0888  0896 

0904 

0913 

0921 

0929 

0938 

0946 

66 

1 

2 

2  3  4 

24 

0946 

0955 

0963 

0972  0981 

0989 

0998 

1007 

1016 

1025 

1034 

65 

1 

2 

3  3  4 

25 

1034 

1043 

1052 

1061  1070 

1079 

1089 

1098 

1107 

1117 

1126 

64 

1 

2 

3  4  5 

26 

1126 

1136 

1145 

1155  1164 

1174 

1184 

1194 

1203 

1213 

1223 

63 

1 

2 

3  4  5 

27 

1223 

1233 

1243 

1253  1264 

1274 

1284 

1294 

1305 

1315 

1326 

62 

1 

2 

3  4  5 

28 

1326 

1336 

1347 

1357  1368 

1379 

1390 

1401 

1412 

1423 

1434 

61 

1 

2 

3  4  5 

29 

1434 

1445 

1456 

1467  1478 

1490 

1501 

1512 

1524 

1535 

1.1547 

<8(Q>° 

1 

2 

3  5  6 

30° 

1.1547 

1559 

1570 

1582  1594 

1606 

1618 

1630 

1642 

1654 

1666 

59 

1 

2 

4  5  6 

31 

1666 

1679 

1691 

1703  1716 

1728 

1741 

1753 

1766 

1779 

1792 

58 

1 

3 

4  5  6 

32 

1792 

1805 

1818 

1831  1844 

1857 

1870 

1883 

1897 

1910 

1924 

57 

1 

3 

4  5  7 

33 

1924 

1937 

1951 

1964  1978 

1992 

2006 

2020 

2034 

2048 

2062 

56 

1 

3 

4  6  7 

34 

2062 

2076 

2091 

2105  2120 

2134 

2149 

2163 

2178 

2193 

2208 

55 

1 

3 

4  6  7 

35 

2208 

2223 

2238 

2253  2268 

2283 

2299 

2314 

2329 

2345 

2361 

54 

2 

3 

5  6  8 

36 

2361 

2376 

2392 

2408  2424 

2440 

2456 

2472 

2489 

2505 

2521 

53 

2 

3 

5  6  8 

37 

2521 

2538 

2554 

2571  2588 

2605 

2622 

2639 

2656 

2673 

2690 

52 

2 

3 

5  7  8 

38 

2690 

2708 

2725 

2742  2760 

2778 

2796 

2813 

2831 

2849 

2868 

51 

2 

4 

5  7  9 

39 

2868 

2886 

2904 

2923  2941 

2960 

2978 

2997 

3016 

3035 

1.3054 

50° 

2 

4 

6  7  9 

40° 

1.3054 

3073 

3093 

3112  3131 

3151 

3171 

3190 

3210 

3230 

3250 

49 

2 

4 

6  810 

41 

3250 

3270 

3291 

3311  3331 

3352 

3373 

3393 

3414 

3435 

3456 

48 

2 

4 

6  810 

42 

3456 

3478 

3499 

3520  3542 

3563 

3585 

3607 

3629 

3651 

3673 

47 

2 

4 

7  9  11 

43 

3673 

3696 

3718 

3741  3763 

3786 

3809 

3832 

3855 

3878 

3902 

46 

2 

5 

7  911 

44 

3902 

3925 

3949 

3972  3996 

4020 

4044 

4069 

4093 

4118 

1.4142 

4B° 

2 

5 

71012 

45° 

1.4142 

(12) 


Secant 

Cosec&nafc 

' 

JO 

J 

J© 

:t 

M 

M 

.4 

.6 

,7 

2  .1 

.8        -9   1 

JO 

45° 

Tenths  of  the 
Tabular  Differenca 
12  3  4  5 

2 

.3 

A 

.5 

1.4142 

45° 

1.4142 

4167 

4192 

4217 

4242 

4267 

4293 

4318 

4344   4370 

4396 

44 

3    5    8  1013 

46 

4396 

4422 

4448 

4474 

4501 

4527 

4554 

4581 

4608   4635 

4663 

43 

3    5    8  1113 

47 

4663 

4690 

4718 

4746 

4774 

4802 

4830 

4859 

4887    4916 

4945 

42 

3    6    8  1114 

48 

4945 

4974 

5003 

5032 

5062 

5092 

5121 

5151 

5182    5212 

5243 

41 

3    6    9  12  15 

49 

5243 

5273 

5304 

5335 

5366 

5398 

5429 

5461 

5493   5525 

1.5557 

40° 

3    6    9  13  16 

50° 

1.5557 

5590 

5622 

5655 

5688 

5721 

5755 

5788 

5822    5856 

5890 

39 

3    710  13  17 

51 

5890 

5925 

5959 

5994 

6029 

6064 

6099 

6135 

6171   6207 

6243 

38 

4    7  11  14  18 

52 

6243 

6279 

6316 

6353 

6390 

6427 

6464 

6502 

6540   6578 

6616 

37 

4    7  11  15  19 

53 

6616 

6655 

6694 

6733 

6772 

6812 

6852 

6892 

6932    6972 

7013 

36 

4    8  12  16  20 

54 

7013 

7054 

7095 

7137 

7179 

7221 

7263 

7305 

7348   7391 

1.7434 

35 

4    8  13  17  21 

55 

1.7434 

7478 

7522 

7566 

7610 

7655 

7700 

7745 

7791    7837 

7883 

34 

4    9  13  18  22 

56 

7883 

7929 

7976 

8023 

8070 

8118 

8166 

8214 

8263    8312 

8361 

33 

5  10  14  19  24 

57 

8361 

8410 

8460 

8510 

8561 

8612 

8663 

8714 

8766   8818 

8871 

32 

5  10  15  20  26 

58 

8871 

8924 

8977 

9031 

9084 

9139 

9194 

9249 

9304   9360 

1.9416 

31 

5  1116  22  27 

59 

60° 

1.9416 

9473 

9530 

9587 

9645 

9703 

9762 

9821 

9880   9940J 

2.0000 

3©° 

29 

6  12  18  23  29 

2.000 

2.006 

2.012 

2.018 

2.025 

2.031 

2.037 

2.043 

2.050  2.056 

2.063 

112    3    3 

61 

2.063 

2.069 

2.076 

2.082 

2.089 

2.096 

2.103 

2.109 

2.116  2.123 

2.130 

28 

112    3    3 

62 

2.130 

2.137 

2.144 

2.151 

2.158 

2.166 

2.173 

2.180 

2.188  2.195 

2.203 

27 

112    3    4 

63 

2.203 

2.210 

2.218 

2.226 

2.233 

2.241 

2.249 

2.257 

2.265   2.273 

2.281 

26 

12    2    3    4 

64 

2.281 

2.289 

2.298 

2.306 

2.314 

2.323 

2.331 

2.340 

2.349  2.357 

2.366 

25 

12    3    3    4 

65 

2.366 

2.375 

2.384 

2.393 

2.402 

2.411 

2.421 

2.430 

2.439  2.449 

2.459 

24 

12    3    4    5 

66 

2.459 

2.468 

2.478 

2.488 

2.498 

2.508 

2.518 

2.528 

2.538  2.549 

2.559 

23 

12    3    4    5 

67 

2.559 

2.570 

2.581 

2.591 

2.602 

2.613 

2.624 

2.635 

2.647  2.658 

2.669 

22 

12    3    4    6 

68 

2.669 

2.681 

2.693 

2.705 

2.716 

2.729 

2.741 

2.753 

2.765  2.778 

2.790 

21 

12    4    5    6 

69 

2.790 

2.803 

2.816 

2.829 

2.842 

2.855 

2.869 

2.882 

2.896  2.910 

2.924 

20° 

13    4    5    7 

70° 

2.924 

2.938 

2.952 

2.967 

2.981 

2.996 

3.011 

3.026 

3.041  3.056 

3.072 

19 

13    4    6    7 

71 

3.072 

3.087 

3.103 

3.119 

3.135 

3.152 

3.168 

3.185 

3.202  3.219 

3.236 

18 

2    3    5    7    8 

72 

3.236 

3.254 

3.271 

3.289 

3.307 

3.326 

3.344 

3.363 

3.382  3.401 

3.420 

17 

2    4    6    7    9 

73 

3.420 

3.440 

3.460 

3.480 

3.500 

3.521 

3.542 

3.563 

3.584  3.606 

3.628 

16 

2    4    6    8  10 

74 

3.628 

3.650 

3.673 

3.695 

3.719 

3.742 

3.766 

3.790 

3.814  3.839 

3.864 

15 

2    5    7    9  12 

75 

3.864 

3.889 

3.915 

3.941 

3.967 

3.994 

4.021 

4.049 

4.077  4.105 

4.134 

14 

3    5    8  11  13 

76 
77 

4.134 

4.445 

4.163 
4.479 

4.192 
4.514 

4.222 
4.549 

4.253 
4.584 

4.284 
4.620 

4.315 
4.657 

4.347 
4.694 

4.379  4.412 
4.732  4.771 

4.445 
4.810 

13 
12 

3    6    9  12  16 

«,     34—39 

78 

4.810 

4.850 

4.890 

4.931 

4.973 

5.016 

5.059 

5.103 

5.148  5.194 

5.241 

11 

|     40-47 

79 

5.241 

5.288 

5.337 

5.386 

5.436 

5.487 

5.540 

5.593 

5.647  5.702 

5.759 

10° 

I     47-57 

3= 

80° 

5.759 

5.816 

5.875 

5.935 

5.996 

6.059 

6.123 

6.188 

6.255   6.323 

6.392 

9 

=     57—69 

81 

6.392 

6.464 

6.537 

6.611 

6.687 

6.765 

6.845 

6.927 

7.011  7.097 

7.185 

8 

"2     72~88 

82 

7.185 

7.276 

7.368 

7.463 

7.561 

7.661 

7.764 

7.870 

7.979  8.091 

8.206 

7 

|    91-115 

83 
84 

8.206 
9.567 

8.324 
9.728 

8.446 
9.895 

8.571 
10.068 

8.700 
10.248 

8.834 
10.433 

8.971 
10.626 

9.113 
10.826 

9.259  9.411 
11.034  11.249 

9.567 
11.474 

6 
5 

°=  118—156 

Interpolation 

85 

11.474 

11.707 

11.951 

12.204 

12.469 

12.745 

13.035 

13.337 

13.654  13.987 

14.336 

4 

accurate,  except 

86 
87 

14.336 
19.11 

14.703 
19.77 

15.089 
20.47 

15.496 
21.23 

15.926 
22.04 

16.380 
22.93 

16.862 
23.88 

17.372 

24.92 

17.914  18.492 
26.05  27.29 

19.107 
28.65 

3 

2 

the  last  figure 

Interpolation 
not  accurate 

88 

28.65 

30.16 

31.84 

33.71 

35.81 

38.20 

40.93 

44.08 

47.75   52.09 

57.30 

1 

89 

57.30 

63.66 

71.62 

81.85 

95.49 

114.59 

143.24 

191.0 

286.5   573.0 

00 

0° 

90° 

00 

U3) 


ad 


« 


<5 


c 


sc 


W 


r* 


,e* 


V1 


05 


t*2 


sp 


*c 


^ 


Log 

1.00 

0 

1 

3 

3 

4 

5 

6 

7 

8 

9 

10 

0.0000 

0004 

0009 

0013 

0017 

0022 

0026 

0030 

0035 

0039 

0043 

1.01 

0043 

0048 

0052 

0056 

0060 

0065 

0069 

0073 

0077 

0082 

0086 

1.02 

0086 

0090 

0095 

0099 

0103 

0107 

0111 

0116 

0120 

0124 

0128 

1.03 

0128 

0133 

0137 

0141 

0145 

0149 

0154 

0158 

0162 

0166 

0170 

1.04 

0170 

0175 

0179 

0183 

0187 

0191 

0195 

0199 

0204 

0208 

0212 

1.05 

0212 

0216 

0220 

0224 

0228 

0233 

0237 

0241 

0245 

0249 

0253 

1.06 

0253 

0257 

0261 

0265 

0269 

0273 

0278 

0282 

0286 

0290 

0294 

1.07 

0294 

0298 

0302 

0306 

0310 

0314 

0318 

0322 

0326 

0330 

0334 

1.08 

0334 

0338 

0342 

0346 

0350 

0354 

0358 

0362 

0366 

0370 

0374 

1.09 

0374 

0378 

0382 

0386 

0390 

0394 

0398 

0402 

0406 

0410 

0414 

1.10 

0.0414 

0418 

0422 

0426 

0430 

0434 

0438 

0441 

0445 

0449 

0453 

1.11 

0453 

0457 

0461 

0465 

0469 

0473 

0477 

0481 

0484 

0488 

0492 

1.12 

0492 

0496 

0500 

0504 

0508 

0512 

0515 

0519 

0523 

0527 

0531 

1.13 

0531 

0535 

0538 

0542 

0546 

0550 

0554 

0558 

0561 

0565 

0569 

1.14 

0569 

0573 

0577 

0580 

0584 

0588 

0592 

0596 

0599 

0603 

0607 

1.15 

0607 

0611 

0615 

0618 

0622 

0626 

0630 

0633 

0637 

0641 

0645 

1.16 

0645 

0648 

0652 

0656 

0660 

0663 

0667 

0671 

0674 

0678 

0682 

1.17 

0682 

0686 

0689 

0693 

0697 

0700 

0704 

0708 

0711 

0715 

0719 

1.18 

0719 

0722 

0726 

0730 

0734 

0737 

0741 

0745 

0748 

0752 

0755 

1.19 

0755 

0759 

0763 

0766 

0770 

0774 

0777 

0781 

0785 

0788 

0792 

1.20 

0.0792 

0795 

0799 

0803 

0806 

0810 

0813 

0817 

0821 

0824 

0828 

1.21 

0828 

0831 

0835 

0839 

0842 

0846 

0849 

0853 

0856 

0860 

0864 

1.22 

0864 

0867 

0871 

0874 

0878 

0881 

0885 

0888 

0892 

0896 

0899 

1.23 

0899 

0903 

0906 

0910 

0913 

0917 

0920 

0924 

0927 

0931 

0934 

1.24 

0934 

0938 

0941 

0945 

0948 

0952 

0955 

0959 

0962 

0966 

0969 

1.25 

0969 

0973 

0976 

0980 

0983 

0986 

0990 

0993 

0997 

1000 

1004 

1.26 

1004 

1007 

1011 

1014 

1017 

1021 

1024 

1028 

1031 

1035 

1038 

1.27 

1038 

1041 

1045 

1048 

1052 

1055 

1059 

1062 

1065 

1069 

1072 

1.28 

1072 

1075 

1079 

1082 

1086 

1089 

1092 

1096 

1099 

1103 

1106 

1.29 

1106 

1109 

1113 

1116 

1119 

1123 

1126 

1129 

1133 

1136 

1139 

1.30 

0.1139 

1143 

1146 

1149 

1153 

1156 

1159 

1163 

1166 

1169 

1173 

1.31 

1173 

1176 

1179 

1183 

1186 

1189 

1193 

1196 

1199 

1202 

1206 

1.32 

1206 

1209 

1212 

1216 

1219 

1222 

1225 

1229 

1232 

1235 

1239 

1.33 

1239 

1242 

1245 

1248 

1252 

1255 

1258 

1261 

1265 

1268 

1271 

1.34 

1271 

1274 

1278 

1281 

1284 

1287 

1290 

1294 

1297 

1300 

1303 

1.35 

1303 

1307 

1310 

1313 

1316 

1319 

1323 

1326 

1329 

1332 

1335 

1.36 

1335 

1339 

1342 

1345 

1348 

1351 

1355 

1358 

1361 

1364 

1367 

1.37 

1367 

1370 

1374 

1377 

1380 

1383 

1386 

1389 

1392 

1396 

1399 

1.38 

1399 

1402 

1405 

1408 

1411 

1414 

1418 

1421 

1424 

1427 

1430 

1.39 

1430 

1433 

1436 

1440 

1443 

1446 

1449 

1452 

1455 

1458 

1461 

1.40 

0.1461 

1464 

1467 

1471 

1474 

1477 

1480 

1483 

1486 

1489 

1492 

1.41 

1492 

1495 

1498 

1501 

1504 

1508 

1511 

1514 

1517 

1520 

1523 

1.42 

1523 

1526 

1529 

1532 

1535 

1538 

1541 

1544 

1547 

1550 

1553 

1.43 

1553 

1556 

1559 

1562 

1565 

1569 

1572 

1575 

1578 

1581 

1584 

1.44 

1584 

1587 

1590 

1593 

1596 

1599 

1602 

1605 

1608 

1611 

1614 

1.45 

1614 

1617 

1620 

1623 

1626 

1629 

1632 

1635 

1638 

1641 

1644 

1.46 

1644 

1647 

1649 

1652 

1655 

1658 

1661 

1664 

1667 

1670 

1673 

1.47 

1673 

1676 

1679 

1682 

1685 

1688 

1691 

1694 

1697 

1700 

1703 

1.48 

1703 

1706 

1708 

1711 

1714 

1717 

1720 

1723 

1726 

1729 

1732 

1.49 

1732 

1735 

1738 

1741 

1744 

1746 

1749 

1752 

1755 

1758 

1761 

(14) 


Log 


1.50 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

0.1761 

1764 

1767 

1770 

1772 

1775 

1778 

1781 

1784 

1787 

1790 

1.51 

1790 

1793 

1796 

1798 

1801 

1804 

1807 

1810 

1813 

1816 

1818 

1.52 

1818 

1821 

1824 

1827 

1830 

1833 

1836 

1838 

1841 

1844 

1847 

1.53 

1847 

1850 

1853 

1855 

1858 

1861 

1864 

1867 

1870 

1872 

1875 

1.54 

1875 

1878 

1881 

1884 

1886 

1889 

1892 

1895 

1898 

1901 

1903 

1.55 

1903 

1906 

1909 

1912 

1915 

1917 

1920 

1923 

1926 

1928 

1931 

1.56 

1931 

1934 

1937 

1940 

1942 

1945 

1948 

1951 

1953 

1956 

1959 

1.57 

1959 

1962 

1965 

1967 

1970 

1973 

1976 

1978 

1981 

1984 

1987 

1.58 

1987 

1989 

1992 

1995 

1998 

2000 

2003 

2006 

2009 

2011 

2014 

1.59 

2014 

2017 

2019 

2022 

2025 

2028 

2030 

2033 

2036 

2038 

2041 

1.60 

0.2041 

2044 

2047 

2049 

2052 

2055 

2057 

2060 

2063 

2066 

2068 

1.61 

2068 

2071 

2074 

2076 

2079 

2082 

2084 

2087 

2090 

2092 

2095 

1.62 

2095 

2098 

2101 

2103 

2106 

2109 

2111 

2114 

2117 

2119 

2122 

1.63 

2122 

2125 

2127 

2130 

2133 

2135 

2138 

2140 

2143 

2146 

2148 

1.64 

2148 

2151 

2154 

2156 

2159 

2162 

2164 

2167 

2170 

2172 

2175 

1.65 

2175 

2177 

2180 

2183 

2185 

.2188 

2191 

2193 

2196 

2198 

2201 

1.66 

2201 

2204 

2206 

2209 

2212 

2214 

2217 

2219 

2222 

2225 

2227 

1.67 

2227 

2230 

2232 

2235 

2238 

2240 

2243 

2245 

2248 

2251 

2253 

1.68 

2253 

2256 

2258 

2261 

2263 

2266 

2269 

2271 

2274 

2276 

2279 

1.69 

2279 

2281 

2284 

2287 

2289 

2292 

2294 

2297 

2299 

2302 

2304 

1.70 

0.2304 

2307 

2310 

2312 

2315 

2317 

2320 

2322 

2325 

2327 

2330 

1.71 

2330 

2333 

2335 

2338 

2340 

2343 

2345 

2348 

2350 

2353 

2355 

1.72 

2355 

2358 

2360 

2363 

2365 

2368 

2370 

2373 

2375 

2378 

2380 

1.73 

2380 

2383 

2385 

2388 

2390 

2393 

2395 

2398 

2400 

2403 

2405 

1.74 

2405 

2408 

2410 

2413 

2415 

2418 

2420 

2423 

2425 

2428 

2430 

1.75 

2430 

2433 

2435 

2438 

2440 

2443 

2445 

2448 

2450 

2453 

2455 

1.76 

2455 

2458 

2460 

2463 

2465 

2467 

2470 

2472 

2475 

2477 

2480 

1.77 

2480 

2482 

2485 

2487 

2490 

2492 

2494 

2497 

2499 

2502 

2504 

1.78 

2504 

2507 

2509 

2512 

2514 

2516 

2519 

2521 

2524 

2526 

2529 

1.79 

2529 

2531 

2533 

2536 

2538 

2541 

2543 

2545 

2548 

2550 

2553 

1.80 

0.2553 

2555 

2558 

2560 

2562 

2565 

2567 

2570 

2572 

2574 

2577 

1.81 

2577 

2579 

2582 

2584 

2586 

2589 

2591 

2594 

2596 

2598 

2601 

1.82 

2601 

2603 

2605 

2608 

2610 

2613 

2615 

2617 

2620 

2622 

2625 

1.83 

2625 

2627 

2629 

2632 

2634 

2636 

2639 

2641 

2643 

2646 

2648 

1.84 

2648 

2651 

2653 

2655 

2658 

2660 

2662 

2665 

2667 

2669 

2672 

1.85 

2672 

2674 

2676 

2679 

2681 

2683 

2686 

2688 

2690 

2693 

2695 

1.86 

2695 

2697 

2700 

2702 

2704 

2707 

2709 

2711 

2714 

2716 

2718 

1.87 

2718 

2721 

2723 

2725 

2728 

2730 

2732 

2735 

2737 

2739 

2742 

1.88 

2742 

2744 

2746 

2749 

2751 

2753 

2755 

2758 

2760 

2762 

2765 

1.89 

2765 

2767 

2769 

2772 

2774 

2776 

2778 

2781 

2783 

2785 

2788 

1.90 

0.2788 

2790 

2792 

2794 

2797 

2799 

2801 

2804 

2806 

2808 

2810 

1.91 

2810 

2813 

2815 

2817 

2819 

2822 

2824 

2826 

2828 

2831 

2833 

1.92 

2833 

2835 

2838 

2840 

2842 

2844 

2847 

2849 

2851 

2853 

2856 

1.93 

2856 

2858 

2860 

2862 

2865 

2867 

2869 

2871 

2874 

2876 

2878 

1.94 

2878 

2880 

2882 

2885 

2887 

2889 

2891 

2894 

2896 

2898 

2900 

1.95 

2900 

2903 

2905 

2907 

2909 

2911 

2914 

2916 

2918 

2920 

2923 

1.96 

2923 

2925 

2927 

2929 

2931 

2934 

2936 

2938 

2940 

2942 

2945 

1.97 

2945 

2947 

2949 

2951 

2953 

2956 

2958 

2960 

2962 

2964 

2967 

1.98 

2967 

2969 

2971 

2973 

2975 

2978 

2980 

2982 

2984 

2986 

2989 

1.99 

2989 

2991 

2993 

2995 

2997 

2999 

3002 

3004 

3006 

3008 

3010 

(15)-. 


& 


/Tog  sin&Tog  cos\         /log  tan  a  log  ctn\ 


M' 


1$ 


These  two  pages  give  the  common  logarithms  of  numbers  between  1  and  10,  correct  to  four 
places.  Moving  the  decimal  point  n  places  to  the  right  (or  left)  in  the  number  is  equivalent 
to  adding  n  (or  —  n)  to  the  logarithm.     Thus,    log  0.017453  =  0.2419  —  2  [  =  2.2419  ]. 


M: 


For  any  Angle  x, 

log  (x  in  radians)  = 

2.2419  +  log  (x°) 


When  x  is  between  0°  and  l°.l 
log  sin  x  =  2.2419  +  log  (x°) 
log  tan  x  =  2.2419  +  log  (x°) 
log  cot  x  —  1.7581  —  log  (x°) 


When  x  is  between  88°.9  and  90° 
log  cos  x  =  2.2419  +  log  (90°— x°) 
log  cot  x  =  2.2419  +  log  (90°— x°) 
log  tan  x  =  1.7581  — log  (90°—x°) 


Log 


it 
c 


0* 


i* 


t<» 


rcC 


l>°° 


1.0 

0 

1 

3 

3 

4 

5 

6 

7 

8 

9 

10 

0.0000 

0043 

0086 

0128 

0170 

0212 

0253 

0294 

0334 

0374 

0414 

1.1 

0414 

0453 

0492 

0531 

0569 

0607 

0645 

0682 

0719 

0755 

0792 

1.2 

0792 

0828 

0864 

0899 

0934 

0969 

1004 

1038 

i072 

1106 

1139 

1.3 

1139 

1173 

1206 

1239 

1271 

1303 

1335 

1367 

1399 

1430  . 

1461 

1.4 

1461 

1492 

1523 

1553 

1584 

1614 

1644 

1673 

1703 

1732 

1761 

1.5 

1761 

1790 

1818 

1847 

1875 

1903 

1931 

1959 

1987 

2014 

2041 

1.6 

2041 

2068 

2095 

2122 

2148 

2175 

2201 

2227 

2253 

2279 

2304 

1.7 

2304 

2330 

2355 

2380 

2405 

2430 

2455 

2480 

2504 

2529 

2553 

1.8 

2553 

2577 

2601 

2625 

2648 

2672 

2695 

2718 

2742 

2765 

2788 

1.9 

2788 

2810 

2833 

2856 

2878 

2900 

2923 

2945 

2967 

2989 

3010 

2.0 

0.3010 

3032 

3054 

3075 

3096 

3118 

3139 

3160 

3181 

3201 

3222 

2.1 

3222 

3243 

3263 

3284 

3304 

3324 

3345 

3365 

3385 

3404 

3424 

2.2 

3424 

3444 

3464 

3483 

3502 

3522 

3541 

3560 

3579 

3598 

3617 

2.3 

3617 

3636 

3655 

3674 

3692 

3711 

3729 

3747 

3766 

3784 

3802 

2.4 

3802 

3820 

3838 

3856 

3874 

3892 

3909 

3927 

3945 

3962 

3979 

2.5 

3979 

3997 

4014 

4031 

4048 

4065 

4082 

4099 

4116 

4133 

4150 

2.6 

4150 

4166 

4183 

4200 

4216 

4232 

4249 

4265 

4281 

4298 

4314 

2.7 

4314 

4330 

4346 

4362 

4378 

4393 

4409 

4425 

4440 

4456 

4472 

2.8 

4472 

4487 

4502 

4518 

4533 

4548 

4564 

4579 

4594 

4609 

4624 

2.9 

4624 

4639 

4654 

4669 

4683 

4698 

4713 

4728 

4742 

4757 

4771 

3.0 

0.4771 

4786 

4800 

4814 

4829 

4843 

4857 

4871 

4886 

4900 

4914 

3.1 

4914 

4928 

4942 

4955 

4969 

4983 

4997 

5011 

5024 

5038 

5051 

3.2 

5051 

5065 

5079 

5092 

5105 

5119 

5132 

5145 

5159 

5172 

5185 

3.3 

5185 

5198 

5211 

5224 

5237 

5250 

5263 

5276 

5289 

5302 

5315 

3.4 

5315 

5328 

5340 

5353 

5366 

5378 

5391 

5403 

5416 

5428 

5441 

3.5 

5441 

5453 

5465 

5478 

5490 

5502 

5514 

5527 

5539 

5551 

5563 

3.6 

5563 

5575 

5587 

5599 

5611 

5623 

5635 

5647 

5658 

5670 

5682 

3.7 

5682 

5694 

5705 

5717 

5729 

5740 

5752 

5763 

5775 

5786 

5798 

3.8 

5798 

5809 

5821 

5832 

5843 

5855 

5866 

5877 

5888 

5899 

5911 

3.9 

5911 

5922 

5933 

5944 

5955 

5966 

5977 

5988 

5999 

6010 

6021 

4.0 

0.6021 

6031 

6042 

6053 

6064 

6075 

6085 

6096 

6107 

6117 

6128 

4.1 

6128 

6138 

6149 

6160 

6170 

6180 

6191 

6201 

6212 

6222 

6232 

4.2 

6232 

6243 

6253 

6263 

6274 

6284 

6294 

6304 

6314 

6325 

6335 

4.3 

6335 

6345 

6355 

6365 

6375 

6385 

6^95 

6405 

6415 

6425 

6435 

4.4 

6435 

6444 

6454 

6464 

6474 

6484 

6493 

6503 

6513 

6522 

6532 

4.5 

6532 

6542 

6551 

6561 

6571 

6580 

6590 

6599 

6609 

6618 

6628 

4.6 

6628 

6637 

6646 

6656 

6665 

6675 

6684 

6693 

6702 

6712 

6721 

4.7 

6721 

6730 

6739 

6749 

6758 

6767 

6776 

6785 

6794 

6803 

6812 

4.8 

6812 

6821 

6830 

6839 

6848 

6857 

6866 

6875 

6884 

6893 

6902 

4.9 

6902 

6911 

6920 

6928 

6937 

6946 

6955 

6964 

6972 

6981 

6990 

Tenths  of  the 
Tabular  Difference 

12  3  4  5 


To  avoid  interpo- 
lation in  the  first 
ten  lines,  use  the 
special  table  on  the 
preceding  page. 


2    4  6  811 

2    4  6  810 

2    4  6  810 

2    4  5  7    9 

2    4  5  7    9 

2    3  5  7    9 

2    3  5  7   8 

2    3  5  6    8 

2    3  5  6    8 

13  4  6    7 

13  4  6    7 

1    3  4  6    7 

13  4  5    7 

13  4  5    6 

13  4  5    6 

12  4  5    6 

12  4  5    6 

12  3  5    6 

12  3  5    6 

12  3  4    6 

12  3  4   5 

12  3  4    5 

12  3  4    5 

12  3  4    5 

12  3  4    5 

12  3  4    5 

12  3  4    5 

12  3  4    5 

12  3  4    4 

12  3  4   4 


log  tr  =  0.4971 
log  e  =  0.4343 


log  w/2==  0.1961 


log  IT2 

(16) 


■■  0.9943  log\AT=  0.2486 

log  (0.434^  =1.6378 


Log 


5.0 

0 

1 

3 

3 

4 

5 

6 

7 

S   9 

10 

0.6990 

6998 

7007 

7016 

7024 

7033 

7042 

7050 

7059  7067 

7076 

5.1 

7076 

7084 

7093 

7101 

7110 

7118 

7126 

7135 

7143  7152 

7160 

5.2 

7160 

7168 

7177 

7185 

7193 

7202 

7210 

7218 

7226  7235 

7243 

5.3 

7243 

7251 

7259 

7267 

7275 

7284 

7292 

7300 

7308  7316 

7324 

5.4 

7324 

7332 

7340 

7348 

7356 

7364 

7372 

7380 

7388  7396 

7404 

5.5 

7404 

7412 

7419 

7427 

7435 

7443 

7451 

7459 

7466  7474 

7482 

5.6 

7482 

7490 

7497 

7505 

7513 

7520 

7528 

7536 

7543  7551 

7559 

5.7 

7559 

7566 

7574 

7582 

7589 

7597 

7604 

7612 

7619  7627 

7634 

5.8 

7634 

7642 

7649 

7657 

7664 

7672 

7679 

7686 

7694  7701 

7709 

5.9 

7709 

7716 

7723 

7731 

7738 

7745 

7752 

7760 

7767  7774 

7782 

6.0 

0.7782 

7789 

7796 

7803 

7810 

7818 

7825 

7832 

7839  7846 

7853 

6.1 

7853 

7860 

7868 

7875 

7882 

7889 

7896 

7903 

7910  7917 

7924 

6.2 

7924 

7931 

7938 

7945 

7952 

7959 

7966 

7973 

7980  7987 

7993 

6.3 

7993 

8000 

8007 

8014 

8021 

8028 

8035 

8041 

8048  8055 

8062 

6.4 

8062 

8069 

8075 

8082 

8089 

8096 

8102 

8109 

8116  8122 

8129 

6.5 

8129 

8136 

8142 

8149 

8156 

8162 

8169 

8176 

8182  8189 

8195 

6.6 

8195 

8202 

8209 

8215 

8222 

8228 

8235 

8241 

8248  8254 

8261 

6.7 

8261 

8267 

8274 

8280 

8287 

8293 

8299 

8306 

8312  8319 

8325 

6.8 

8325 

8331 

8338 

8344 

8351 

8357 

8363 

8370 

*8376  8382 

8388 

6.9 

8388 

8395 

8401 

8407 

8414 

8420 

8426 

8432 

8439  8445 

8451 

7.0 

0.8451 

8457 

8463 

8470 

8476 

8482 

8488 

8494 

8500  8506 

8513 

7.1 

8513 

8519 

8525 

8531 

8537 

8543 

8549 

8555 

8561  8567 

8573 

7.2 

8573 

8579 

8585 

8591 

8597 

8603 

8609 

8615 

8621  8627 

8633 

'7.3 

8633 

8639 

8645 

8651 

8657 

8663 

8669 

8675 

8681  8686 

8692 

7.4 

8692 

8698 

8704 

8710 

8716 

8722 

8727 

8733 

8739  8745 

8751 

7.5 

8751 

8756 

8762 

8768 

8774 

8779 

8785 

8791 

8797  8802 

8808 

7.6 

8808 

8814 

8820 

8825 

8831 

8837 

8842 

8848 

8854  8859 

8865 

7.7 

8865 

8871 

8876 

8882 

8887 

8893 

8899 

8904 

8910  8915 

8921 

7.8 

8921 

8927 

8932 

8938 

8943 

8949 

8954 

8960 

8965  8971 

8976 

7.9 

8976 

8982 

8987 

8993 

8998 

9004 

9009 

9015 

9020  9025 

9031 

8.0 

0.9031 

9036 

9042 

9047 

9053 

9058 

9063 

9069 

9074  9079 

9085 

8.1 

9085 

9090 

9096 

9101 

9106 

9112 

9117 

9122 

9128  9133 

9138 

8.2 

9138 

9143 

9149 

9154 

9159 

9165 

9170 

9175 

9180  9186 

9191 

8.3 

9191 

9196 

9201 

9206 

9212 

9217 

9222 

9227 

9232  9238 

9243 

8.4 

9243 

9248 

9253 

9258 

9263 

9269 

9274 

9279 

9284  9289 

9294 

8.5 

9294 

9299 

9304 

9309 

9315 

9320 

9325 

9330 

9335  9340 

9345 

8.6 

9345 

9350 

9355 

9360 

9365 

9370 

9375 

9380 

9385  9390 

9395 

8.7 

9395 

9400 

9405 

9410 

9415 

9420 

9425 

9430 

9435  9440 

9445 

8.8 

9445 

9450 

9455 

9460 

9465 

9469 

9474 

9479 

9484  9489 

9494 

8.9 

9494 

9499 

9504 

9509 

9513 

9518 

9523 

9528 

9533  9538 

9542 

9.0 

0.9542 

9547 

9552 

9557 

9562 

9566 

9571 

9576 

9581  9586 

9590 

9.1 

9590 

9595 

9600 

9605 

9609 

9614 

9619 

9624 

9628  9633 

9638 

9.2 

9638 

9643 

9647 

9652 

9657 

9661 

9666 

9671 

9675  9680 

9685 

9.3 

9685 

9689 

9694 

9699 

9703 

9708 

9713 

9717 

9722  9727 

9731 

9.4 

9731 

9736 

9741 

9745 

9750 

9754 

9759 

9763 

*768  9773 

9777 

9.5 

9777 

9782 

9786 

9791 

9795 

9800 

9805 

9809 

9814  9818 

9823 

9.6 

9823 

9827 

9832 

9836 

9841 

9845 

9850 

9854 

9859  9863 

9868 

9.7 

9868 

9872 

9877 

9881 

9886 

9890 

9894 

9899 

9903  9908 

9912 

9.8 

9912 

9917 

9921 

9926 

9930 

9934 

9939 

9943 

9948  9952 

9956 

9.9 

9956 

9961 

9965 

9969 

9974 

9978 

9983 

9987 

9991  9996 

Tenths  of  the 

abular  Difference 

2  3  4  5 


2  3  3  4 

2  3  3  4 

2  2  3  4 

2  2  3  4 

2  2  3  4 

2  2  3  4 

2  2  3  4 

2  2  3  4 

12  3  4 

12  3  4 

12  3  4 

12  3  4 

12  3  3 

12  3  3 

12  3  3 

12  3  3 

12  3  3 

12  3  3 

12  3  3 

12  3  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

1  2  '2  3 

0  112  2 

0  112  2 

0  112  2 

0  112  2 

0  112  2 

0  112  2 

0  112  2 

0  112  2 

0  112  2 

0  112  2 

0  112  2 

0  112  2 

0  112  2 


(17) 


> 

l 
#» 


~3 
>3 


^ 


/Tog  sin  &  log  cos\ 


BOSTON  COLLEGE  LIBRARY 
ioffcna'ioglffi^  HEX,  MASl 


P 


o' 

,  I' 

Log  Sin 

*       u  u  e      j 

Log  Cos 

r«5 

| 

JD    ©   11      (R 

® 

4  3  2  1    fO) 

Tenths  of  the 
Tabular  Difference 

1     2    3   4 

o°.o 

o  ■ 

5 

6   7   a St 

12  3  4  5 

-oo   4.2419  5429  7190  8439 

9408  J 

0200  0870  1450  1961  3.2419 

89.9 

0.1 

3.2419 

2833  3211  3558  3880 

4180 

4460  4723  4971  5206   5429 

89.8 

To  avoid  interpo- 

0.2 

5429 

5641  5843  6036  6221 

6398 

6568  6732  6890  7043   7190 

89.7 

lation  in  the  first 

c* 

0.3 

7190 

7332  7470  7604  7734 

7859 

7982  8101  8217  8329   8439 

89.6 

eleven  lines,  usa 

| 

0.4 

8439 

8547  8651  8753  8853 

8951 

9046  9140  9231  9321  3.9408 

89.5 

note.* 

0.5 

3.9408 

9494  9579  9661  9743 

9822 

9901  9977 J  0053  0127  2.0200 

89.4 

0.6 

2.0200 

0272  0343  0412  0480 

0548 

0614  0679  0744  0807   0870 

89.3 

(Ordinary  Inter- 
polation would  not 

I  s»5 

0.7 

0870 

0931  0992  1052  1111 

1169 

1227  1284  1340  1395   1450 

89.2 

0.8 

1450 

1503  1557  1609  1661 

1713 

1764  1814  1863  1912   1961 

89.1 

be  accurate  in  the 

C°5 

0.9 

1961 

2009  2056  2103  2150 

2196 

2241  2286  2331  2375  2.2419 

89°.© 

first  three  lines.) 

r.o 

2.2419 

2462  2505  2547  2589 

2630 

2672  2712  2753  2793   2832 

88.9 

i.i 

2832 

2872  2911  2949  2988 

3025 

3063  3100  3137  3174   3210 

88.8 

4  8111519 

1.2 

3210 

3246  3282  3317  3353 

3388 

3422  3456  3491  3524   3558 

88.7 

3  7  10  1417 

1.3 

3558 

3591  3624  3657  3689 

3722 

3754  3786  3817  3848   3880 

88.6 

3  610  13  16 

1.4 

3880 

3911  3941  3972  4002 

4032 

4062  4091  4121  4150  4179 

88.5 

3  6  9  12  15 

1.5 

4179 

4208  4237  4265  4293 

4322 

4349  4377  4405  4432   4459 

88.4 

3  6  8  1114 

1.6 

4459 

4486  4513  4540  4567 

4593 

4619  4645  4671  4697   4723 

88.3 

3  5  8  1113 

K)<3 

1.7 

4723 

4748  4773  4799  4824 

4848 

4873  4898  4922  4947   4971 

88.2 

2  5  710  12 

1.8 

4971 

4995  5019  5043  5066 

5090 

5113  5136  5160  5183   5206 

88.1 

2  5  7  912 

1.9 

5206 

5228  5251  5274  5296 

5318 

5340  5363  5385  5406  2.5428 

gg0.© 

2  4  7  911 

2°.0 

2.5428 

5450  5471  5493  5514 

5535 

5557  5578  5598  5619   5640 

87.9 

2  4  6  811 

2.1 

5640 

5661  5681  5702  5722 

5742 

5762  5782  5802  5822   5842 

87.8 

2  4  6  810 

2.2 

5842 

5862  5881  5901  5920 

5939 

5959  5978  5997  6016   6035 

87.7 

2  4  6  810 

2.3 

6035 

6054  6072  6091  6110 

6128 

6147  6165  6183  6201   6220 

87.6 

2  4  6  7  9 

2.4 

6220 

6238  6256  6274  6291 

6309 

6327  6344  6362  6379   6397 

87.5 

2  4  5  7  9 

2.5 

6397 

6414  6431  6449  6466 

6483 

6500  6517  6534  6550   6567 

87.4 

2  3  5  7  9 

2.6 

6567 

6584  6600  6617  6633 

6650 

6666  6682  6699  6715   6731 

87.3 

2  3  5  7  8 

2.7 

6731 

6747  6763  6779  6795 

6810 

6826  6842  6858  6873   6889 

87.2 

2  3  5  6  8 

2.8 

6889 

6904  6920  6935  6950 

6965 

6981  6996  7011  7026   7041 

87.1 

2  3  5  6  8 

2.9 

7041 

7056  7071  7086  7100 

7115 

7130  7144  7159  7174  2.7188 

87°.© 

13  4  6  7 

3°0 

2.7188 

7202  7217  7231  7245 

7260 

7274  7288  7302  7316   7330 

86.9 

13  4  6  7 

3.1 

7330 

7344  7358  7372  7386 

7400 

7413  7427  7441  7454   7468 

86.8 

13  4  6  7 

3.2 

7468 

7482  7495  7508  7522 

7535 

7549  7562  7575  7588   7602 

86.7 

13  4  5  7 

3-3 

7602 

7615  7628  7641  7654 

7667 

7680  7693  7705  7718   7731 

86.6 

13  4  5  6 

3.4 

7731 

7744  7756  7769  7782 

7794 

7807  7819  7832  7844   7857 

86.5 

13  4  5  6 

3.5 

7857 

7869  7881  7894  7906 

7918 

7930  7943  7955  7967   7979 

86.4 

12  4  5  6 

3.6 

7979 

7991  8003  8015  8027 

8039 

8051  8062  8074  8086   8098 

86.3 

12  4  5  6 

3.7 

8098 

8109  8121  8133  8144 

8156 

8168  8179  8191  8202   8213 

86.2 

12  3  5  6 

3.8 

8213 

8225  8236  8248  8259 

8270 

8281  8293  8304  8315   8326 

86.1 

12  3  5  6 

3.9 

8326 

8337  8348  8359  8370 

8381 

8392  8403  8414  8425  2.8436 

8(3°.© 

12  3  4  5 

4°.0 

2.8436 

8447  8457  8468  8479 

8490 

8500  8511  8522  8532   8543 

85.9 

12  3  4  5 

4.1 

8543 

8553  8564  8575  8585 

8595 

8606  8616  8627  8637   8647 

85.8 

12  3  4  5 

4.2 

8647 

8658  8668  8678  8688 

8699 

8709  8719  8729  8739   8749 

85.7 

12  3  4  5 

4.3 

8749 

8759  8769  8780  8790 

8799 

8809  8819  8829  8839   8849 

85.6 

12  3  4  5 

4.4 

8849 

8859  8869  8878  8888 

8898 

8908  8917  8927  8937   8946 

85.5 

12  3  4  5 

4.5 

8946 

8956  8966  8975  8985 

8994 

9004  9013  9023  9032   9042 

85.4 

12  3  4  5 

4.6 

9042 

9051  9060  9070  9079 

9089 

9098  9107  9116  9126   9135 

85.3 

12  3  4  5 

4.7 

9135 

9144  9153  9162  9172 

9181 

9190  9199  9208  9217   9226 

85.2 

12  3  4  5 

4.8 

9226 

9235  9244  9253  9262 

9271 

9280  9289  9298  9307   9315 

85.1 

12  3  4  4 

4.9 

9315 

9324  9333  9342  9351 

9359 

9368  9377  9386  9394  2.9403 

8S°.(Q 

12  3  4  4 

*  When  x  is  between  0°  and  l°.l  .    [See  page  28]       *  When  x  is  between  88°.9  and  90° 
iog  sin  *  =  log  rad  *  (is)  l°g  cos  *  =  loS  rad  (90  ~x* 


Log  Sin 


5°.0 

5.1 
5.2 
5.3 

5.4 

5.5 
5.6 
5.7 
5.8 
5.9 

6°0 

6.1 
6.2 
6-3 
6.4 


8.5 
8.6 
8.7 
8.8 
8.9 

9°0 

9.1 
9.2 
9.3 
9.4 

9.5 
9.6 
9.7 
9.8 
9.9 


2.9403  9412  9420  9429  9437  9446 

9489  9497  9506  9514  9523  9531 

9573  9581  9589  9598  9606  9614 

9655  9664  9672  9680  9688  9696 

9736  9744  9752  9760  9768  9776 

9816  9824  9831  9839  9847  9855 

9894  9901  9909  9917  9925  9932 

2.9970  9978  9986  9993J0001  0008 

1.0046  0053  0061  0068  0075  0083 

0120  0127  0134  0142  0149  0156 

1.0192  0200  0207  0214  0221  0228 

0264  0271  0278  0285  0292  0299 

0334  0341  0348  0355  0362  0369 

0403  0410  0417  0424  0431  0438 

0472  0478  0485  0492  0498  0505 


6.5 

0539 

0545 

0552 

0558 

0565 

0572 

6.6 

0605 

0611 

0618 

0624 

0631 

0637 

6.7 

0670 

0676 

0683 

0689 

0695 

0702 

6.8 

0734 

0740 

0746 

0753 

0759 

0765 

6.9 

0797 

0803 

0809 

0816 

0822 

0828 

7°.0 

1.0859 

0865 

0871 

0877 

0884 

0890 

7.1 

0920 

0926 

0932 

0938 

0945 

0951 

7.2 

0981 

0987 

0993 

0999 

1005 

1011 

7.3 

1040 

1046 

1052 

1058 

1064 

1070 

7.4 

1099 

1105 

1111 

1116 

1122 

1128 

7.5 

1157 

1163 

1168 

1174 

1180 

1186 

7.6 

1214 

1220 

1226 

1231 

1237 

1242 

7.7 

1271 

1276 

1282 

1287 

1293 

1299 

7.8 

1326 

1332 

1337 

1343 

1348 

1354 

7.9 

1381 

1387 

1392 

1398 

1403 

1409 

8°.0 

1.1436 

1441 

1446 

1452 

1457 

1462 

8.1 

1489 

1494 

1500 

1505 

1510 

1516 

8.2 

1542 

1547 

1553 

1558 

1563 

1568 

8.3 

1594 

1600 

1605 

1610 

1615 

1620 

8.4 

1646 

1651 

1656 

1661 

1666 

1672 

1697  1702  1707  1712  1717  1722 

1747  1752  1757  1762  1767  1772 

1797  1802  1807  1812  1817  1822 

1847  1851  1856  1861  1866  1871 

1895  1900  1905  1910  191S  1919 

1.1943  1948  1953  1958  1962  1967 

1991  1996  2000  2005  2010  2015 

2038  2043  2047  2052  2057  2061 

2085  2089  2094  2098  2103  2108 

2131  2135  2140  2144  2149  2153 

2176  2181  2185  2190  2194  2199 

2221  2226  2230  2235  2239  2243 

2266  2270  2275  2279  2283  2288 

2310  2314  2319  2323  2327  2332 

2353  2358  2362  2367  2371  2375 


9455  9463  9472  9480  2.9489 

9539  9548  9556  9565   9573 

9623  9631  9639  9647   9655 

9704  9712  9720  9728   9736 

9784  9792  9800  9808   9816 

9863  9870  9878  9886   9894 

9940  9948  9955  9963  2.9970 

0016  0023  0031  0038  1.0046 

0090  0098  0105  0112   0120 

0163  0171  0178  0185  T.0192 

0235  0243  0250  0257  0264 

0306  0313  0320  0327  0334 

0376  0383  0390  0397  0403 

0444  0451  0458  0465  0472 

0512  0519  0525  0532  0539 

0578  0585  0591  0598   0605 

0644  0650  0657  0663   0670 

0708  0715  0721  0727   0734 

0772  0778  0784  0790   0797 

0834  0840  0847  0853  T.0859 

0896  0902  0908  0914  0920 

0957  0963  0969  0975  0981 

1017  1022  1028  1034  1040 

1076  1081  1087  1093  1099 

1134  1140  1145  1151  1157 

1191  1197  1203  1208  1214 

1248  1254  1259  1265  1271 

1304  1310  1315  1321  1326 

1359  1365  1370  1376  1381 

1414  1419  1425  1430  1.1436 

1468  1473  1478  1484  1489 

1521  1526  1532  1537  1542 

1574  1579  1584  1589  1594 

1625  1631  1636  1641  1646 

1677  1682  1687  1692  1697 

1727  1732  1737  1742   1747 

1777  1782  1787  1792   1797 

1827  1832  1837  1842   1847 

1876  1881  1886  1890   1895 

1924  1929  1934  1939  T.1943 

1972  1977  1981  1986  1991 

2019  2024  2029  2033  2038 

2066  2071  2075  2080  2085 

2112  2117  2121  2126  2131 

2158  2162  2167  2172  2176 

2203  2208  2212  2217   2221 

2248  2252  2257  2261   2266 

2292  2297  2301  2305   2310 

2336  2340  2345  2349   2353 

2379  2384  2388  2392  1.2397 


84.9 
84.8 
84.7 
84.6 
84.5 

84.4 
84.3 
84.2 
84.1 

M°.d 

83.9 
83.8 
83.7 
83.6 
83.5 

83.4 
83.3 
83.2 
83.1 

82.9 
82.8 
82.7 
82.6 
82.5 

82.4 
82.3 
82.2 
82.1 

82°.0 

81.9 
81.8 
81.7 
81.6 
81.5 

81.4 
81.3 
81.2 
81.1 

ll°.C 

80.9 
80.8 
80.7 
80.6 
80.5 

80.4 
80.3 
80.2 
80.1 


Tenths  of  the 

Tabular  Difference 

12  3  4  5 

12  3  3  4 

12  3  3  4 

12  2  3  4 

12  2  3  4 

12  2  3  4 

12  2  3  4 

12  2  3  4 

12  2  3  4 

112  3  4 

112  3  4 

112  3  4 

112  3  4 

112  3  3 

112  3  3 

112  3  3 

112  3  3 

112  3  3 

112  3  3 

112  3  3 

112  2  3 

112  2  3 

112  2  3 

112  2  3 

112  2  3 

112  2  3 

112  2  3 

112  2  3 

112  2  3 

112  2  3 

112  2  3 

112  2  3 

112  2  3 

112  2  3 

112  2  3 

112  2  3 

112  2  3 

0  112  2 

0  112  2 

0  112  2 

0  112  2 

0  112  2 

0  112  2 

0  112  2 

0  112  2 

0  112  2 

0  112  2 

0  112  2 

0  112  2 

0  112  2 

0  112  2 


ai 


(Xi 


•J 


^ 


M 


1* 


(19) 


IP** 


/r 


log  sin  &  log  cos\         /log  tan  &  log  ctn\ 


\  ...LOG  /      s 


Log  Sin 

hog 

Cos 

,0 

L  .© 

.1 

.2 

.7 

3 

4 

.5 

.4 

.6 

.7 

.8 

.! 

.9  ~ 

B 

§>©° 

-  00 

0° 

—  oo 

3.2419 

5429 

7190 

8439 

9408  J  0200 

0870 

1450 

1961 

2.2419 

89 

1 

2.2419 

2832 

3210 

3558 

3880 

4179 

4459 

4723 

4971 

5206 

5428 

88 

2 

5428 

5640 

5842 

6035 

6220 

6397 

6567 

6731 

6889 

7041 

7188 

87 

3 

7188 

7330 

7468 

7602 

7731 

7857 

7979 

8098 

8213 

8326 

8436 

86 

4 

8436 

8543 

8647 

8749 

8849 

8946 

9042 

9135 

9226 

9315 

2.9403 

85 

5 

2.9403 

9489 

9573 

9655 

9736 

9816 

9894 

9970  J  0046 

0120 

1.0192 

84 

6 

1.0192 

0264 

0334 

0403 

0472 

0539 

0605 

0670 

0734 

0797 

0859 

83 

7 

0859 

0920 

0981 

1040 

1099 

1157 

1214 

1271 

1326 

1381 

1436 

82 

8 

1436 

1489 

1542 

1594 

1646 

1697 

1747 

1797 

1847 

1895 

1943 

81 

9 

1943 

1991 

2038 

2085 

2131 

2176 

2221 

2266 

2310 

2353 

1.2397 

g(0>° 

10° 

1.2397 

2439 

2482 

2524 

2565 

2606 

2647 

2687 

2727 

2767 

2806 

79 

11 

2806 

2845 

2883 

2921 

2959 

2997 

3034 

3070 

3107 

3143 

3179 

78 

12 

3179 

3214 

3250 

3284 

3319 

3353 

3387 

3421 

3455 

3488 

3521 

77 

13 

3521 

3554 

3586 

3618 

3650 

3682 

3713 

3745 

3775 

3806 

3837 

76 

14 

3837 

3867 

3897 

3927 

3957 

3986 

4015 

4044 

4073 

4102 

4130 

75 

15 

4130 

4158 

4186 

4214 

4242 

4269 

4296 

4323 

4350 

4377 

4403 

74 

16 

4403 

4430 

4456 

4482 

4508 

4533 

4559 

4584 

4609 

4634 

4659 

73 

17 

4659 

4684 

4709 

4733 

4757 

4781 

4805 

4829 

4853 

4876 

4900 

72 

18 

4900 

4923 

4946 

4969 

4992 

5015 

5037 

5060 

5082 

5104 

5126 

71 

19 

5126 

5148 

5170 

5192 

5213 

5235 

5256 

5278 

5299 

5320 

1.5341 

70° 

20° 

T.5341 

5361 

5382 

5402 

5423 

5443 

5463 

5484 

5504 

5523 

5543 

69 

21 

5543 

5563 

5583 

5602 

5621 

5641 

5660 

5679 

5698 

5717 

5736 

68 

22 

5736 

5754 

5773 

5792 

5810 

5828 

5847 

5865 

5883 

5901 

5919 

67 

23 

5919 

5937 

5954 

5972 

5990 

6007 

6024 

6042 

6059 

6076 

6093 

66 

24 

6093 

6110 

6127 

6144 

6161 

6177 

6194 

6210 

6227 

6243 

6259 

65 

25 

6259 

6276 

6292 

6308 

6324 

6340 

6356 

6371 

6387 

6403 

6418 

64 

26 

6418 

6434 

6449 

6465 

6480 

6495 

6510 

6526 

6541 

6556 

6570 

63 

27 

6570 

6585 

6600 

6615 

6629 

6644 

6659 

6673 

6687 

6702 

6716 

62 

28 

6716 

6730 

6744 

6759 

6773 

6787 

6801 

6814 

6828 

6842 

6856 

61 

29 

6856 

6869 

6883 

6896 

6910 

6923 

6937 

6950 

6963 

6977 

1.6990 

<S(G>° 

30° 

1.6990 

7003 

7016 

7029 

7042 

7055 

7068 

7080 

7093 

7106 

7118 

59 

31 

7118 

7131 

7144 

7156 

7168 

7181 

7193 

7205 

7218 

7230 

7242 

58 

32 

7242 

7254 

7266 

7278 

7290 

7302 

7314 

7326 

7338 

7349 

7361 

57 

33 

7361 

7373 

7384 

7396 

7407 

7419 

7430 

7442 

7453 

7464 

7476 

56 

34 

7476 

7487 

7498 

7509 

7520 

7531 

7542 

7553 

7564 

7575 

7586 

55 

35 

7586 

7597 

7607 

7618 

7629 

7640 

7650 

7661 

7671 

7682 

7692 

54 

36 

7692 

7703 

7713 

7723 

7734 

7744 

7754 

7764 

7774 

7785 

7795 

53 

37 

7795 

7805 

7815 

7825 

7835 

7844 

7854 

7864 

7874 

7884 

7893 

52 

38 

7893 

7903 

7913 

7922 

7932 

7941 

7951 

7960 

7970 

7979 

7989 

51 

39 

7989 

7998 

8007 

8017 

8026 

8035 

8044 

8053 

8063 

8072 

1.8081 

so° 

40° 

1.8081 

8090 

8099 

8108 

8117 

8125 

8134 

8143 

8152 

8161 

8169 

49 

41 

8169 

8178 

8187 

8195 

8204 

8213 

8221 

8230 

8238 

8247 

8255 

48 

42 

8255 

8264 

8272 

8280 

8289 

8297 

8305 

8313 

8322 

8330 

8338 

47 

43 

8338 

8346 

8354 

8362 

8370 

8378 

8386 

8394 

8402 

8410 

8418 

46 

44 

8418 

8426 

8433 

8441 

8449 

8457 

8464 

8472 

8480 

8487 

1.8495 

45° 

45° 

1.8495 

Tenths  of  the 
Tabular  Difference 

12  3   4   5 

To  avoid  interpo- 
lation in  the  first 
ten  lines,  use  the 
special  table  on  the 
preceding  page. 

(Ordinary  inter- 
polation would  not 
be  accurate  in  the 
first  three  lines.) 

4  8  12  16  20 

4  7  11 15  19 

3  710  1417 

3  6  9  13  16 

3  6  9  12  15 

3  5  8  1114 

3  5  8  1013 

2  5  710  12 

2  5  7  911 

2  4  6  911 

2  4  6  8  10 

2  4  6  810 

2  4  5  7  9 

2  3  5  7  9 

2  3  5  7  8 

2  3  5  6  8 

2  3  5  6  8 

13  4  6  7 
13  4  6  7 
13  4  5  7 

13  4  5  6 

12  4  5  6 

12  4  5  6 

12  3  5  6 

12  3  4  6 

12  3  4  5 

12  3  4  5 

12  3  4  5 

12  3  4  5 

12  3  4  5 

12  3  4  4 

12  3  3  4 

12  2  3  4 

12  2  3  4 

12  2  3  4 


(20) 


Log  Sin 


Log  Cos 


45° 

46 
47 
48 
49 

50° 

51 
52 
53 
54 

55 
56 
57 
58 
59 

60° 

61 
62 
63 
64 

65 
66 
67 
68 
69 

70° 

71 
72 
73 
74 

75 
76 
77 
78 
79 

80° 

81 
82 
83 
84 

85 
86 

87 
88 
89 

90° 


1.8495  8502  8510  8517  8525  8532 

8569  8577  8584  8591  8598  8606 

8641  8648  8655  8662  8669  8676 

8711  8718  8724  8731  8738  8745 

8778  8784  8791  8797  8804  8810 

1.8843  8849  8855  8862  8868  8874 

8905  8911  8917  8923  8929  8935 

8965  8971  8977  8983  8989  8995 

9023  9029  9035  9041  9046  9052 

9080  9085  9091  9096  9101  9107 

9134  9139  9144  9149  9155  9160 

9186  9191  9196  9201  9206  9211 

9236  9241  9246  9251  9255  9260 

9284  9289  9294  9298  9303  9308 

9331  9335  9340  9344  9349  9353 

1.9375  9380  9384  9388  9393  9397 

9418  9422  9427  9431  9435  9439 

9459  9463  9467  9471  9475  9479 

9499  9503  9506  9510  9514  9518 

9537  9540  9544  9548  9551  9555 

9573  9576  9580  9583  9587  9590 

9607  9611  9614  9617  9621  9624 

9640  9643  9647  9650  9653  9656 

9672  9675  9678  9681  9684  9687 

9702  9704  9707  9710  9713  9716 

1.9730  9733  9735  9738  9741  9743 

9757  9759  9762  9764  9767  9770 

9782  9785  9787  9789  9792  9794 

9806  9808  9811  9813  9815  9817 

9828  9831  9833  9835  9837  9839 

9849  9851  9853  9855  9857  9859 

9869  9871  9873  9875  9876  9878 

9887  9889  9891  9892  9894  9896 

9904  9906  9907  9909  9910  9912 

9919  9921  9922  9924  9925  9927 

1.9934  9935  9936  9937  9939  9940 

9946  9947  9949  9950  9951  9952 

9958  9959  9960  9961  9962  9963 

9968  9968  9969  9970  9971  9972 

9976  9977  9978  9978  9979  9980 

9983  9984  9985  9985  9986  9987 

9989  9990  9990  9991  9991  9992 

9994  9994  9995  9995  9996  9996 

9997  9998  9998  9998  9998  9999 

T.9999  9999J0000  0000  0000  0000 

0.0000 


8540  8547  8555  8562  8569 

8613  8620  8627  8634  8641 

8683  8690  8697  8704  8711 

8751  8758  8765  8771  8778 

8817  8823  8830  8836  1.8843 

8880  8887  8893  8899  8905 

8941  8947  8953  8959  8965 

9000  9006  9012  9018  9023 

9057  9063  9069  9074  9080 

9112  9118  9123  9128  9134 

9165  9170  9175  9181  9186 

9216  9221  9226  9231  9236 

9265  9270  9275  9279  9284 

9312  9317  9322  9326  9331 

9358  9362  9367  9371  T.9375 

9401  9406  9410  9414  9418 

9443  9447  9451  9455  9459 

9483  9487  9491  9495  9499 

9522  9525  9529  9533  9537 

9558  9562  9566  9569  9573 

9594  9597  9601  9604  9607 

9627  9631  9634  9637  9640 

9659  9662  9666  9669  9672 

9690  9693  9696  9699  9702 

9719  9722  9724  9727  1.9730 

9746  9749  9751  9754  9757 

9772  9775  9777  9780  9782 

9797  9799  9801  9804  9806 

9820  9822  9824  9826  9828 

9841  9843  9845  9847  9849 

9861  9863  9865  9867  9869 

9880  9882  9884  9885  9887 

9897  9899  9901  9902  9904 

9913  9915  9916  9918  9919 

9928  9929  9931  9932  1.9934 

9941  9943  9944  9945  9946 

9953  9954  9955  9956  9958 

9964  9965  9966  9967  9968 

9973  9974  9975  9975  9976 

9981  9981  9982  9983  9983 

9987  9988  9988  9989  9989 

9992  9993  9993  9994  9994 

9996  9996  9997  9997  9997 

9999  9999  9999  9999  1-9999 

0000  0000  0000  0000  0.0000 


(21) 


44 

.43 

42 

41 

4©c 

39 
38 
37 
36 
35 

34 
33 
32 
31 

3(0)° 

29 
28 
27 
26 
25 

24 
23 
22 
21 

2©° 

19 
18 
17 
16 
15. 

14 
13 
12 
11 

a©° 
9 

8 
7 
6 
5 

4 
3 
2 
1 


Tenths  of  the 
abular  Difference 

2  3  4  5 


12  3  4 

12  3  4 

12  3  3 

12  3  3 

12  3  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

0  112  2 

0  112  2 

0  112  2 

0  112  2 

0  112  2 

0  112  2 

0  112  2 
0  1112 

0  1112 
0  1112 
0  1112 
0  111 
0  111 

0  111 
0  111 
0  0  11 
0  0  11 
0    0    11 

0  0  11 
0  0  1  1 
0  0  11 
0  0  0  1 
0   0   0    1 

0  0  0  1 
0    0   0    0 

0   0   0   0  0 

0   0   0   0  0 

0   0    0   0  0 

0    0    0    0  0 

0    0    0    0  0 

0    0    0    0  0 

0    0    0    0  0 

0   0   0   0  0 


pa 


Q2 


I8K 


w 


t* 


v 


/log  tana  log  ctn\ 


p 


4 


Log  Tan 

Log  C©tai 

o°.o 

0 

1 

2 

_%_     ® 

B 

,4,  g  a 

6*'  7  "  8~ 

!    © 

Tenths  of  the 
Tabular  Difference 

12  3  4  5 

3   4 

5* 

~9   'af 

-  °°   5.2419 

5429 

7190  8439 

9408  J 

0200  0870  1450 

1961  3.2419 

89.9 

To  avoid  interpo- 
lation In  the  first 
eleven  lines,  use 
note.* 

0.1 

3.2419 

2833 

3211 

3558  3880 

4180 

4460  4723  4972 

5206   5429 

89.8 

0.2 

5429 

5641 

5843 

6036  6221 

6398 

6569  6732  6890 

7043   7190 

89.7 

0.3 

7190 

7332 

7470 

7604  7734 

7860 

7982  8101  8217 

8329   8439 

89.6 

0.4 

8439 

8547 

8651 

8754  8853 

8951 

9046  9140  9231 

9321  3.9409 

89.5 

0.5 

3.9409 

9495 

9579 

9662  9743 

9823 

9901  9978J0053 

0127  2.0200 

89.4 

0.6 

0.7 

2.0200 
0870 

0272 
0932 

0343 
0992 

0412  0481 
1052  1111 

0548 
1170 

0614  0680  0744 
1227  1284  1340 

0807   0870 
1395   1450 

89.3 
89.2 

(Ordinary  inter- 
polation would  not 
be  accurate  in  the 
first  three  lines.) 

0.8 
0.9 

1450 
1962 

1504 
2010 

1557 
2057 

1610  1662 
2104  2150 

1713 
2196 

1764  1814  1864 
2242  2287  2331 

1913   1962 
2376  2.2419 

89.1 

gg)°.© 

1°.0 

2.2419 

2462 

2505 

2548  2590 

2631 

2672  2713  2754 

2794   2833 

88.9 

1.1 

2833 

2873 

2912 

2950  2988 

3026 

3064  3101  3138 

3175   3211 

88.8 

4  8  11 15  19 

1.2 

3211 

3247 

3283 

3318  3354 

3389 

3423  3458  3492 

3525   3559 

88.7 

3  710  1417 

1.3 

3559 

3592 

3625 

3658  3691 

3723 

3755  3787  3818 

3850   3881 

88.6 

3  6  10  13  16 

1.4 

3881 

3912 

3943 

3973  4003 

4033 

4063  4093  4122 

4152   4181 

88.5 

3  6  9  12  15 

1.5 

4181 

4210 

4238 

4267  4295 

4323 

4351  4379  4406 

4434   4461 

88.4 

3  6  8  1114 

1.6 

4461 

4488 

4515 

4542  4568 

4595 

4621  4647  4673 

4699   4725 

88.3 

3  5  8  11 13 

1.7 

4725 

4750 

4775 

4801  4826 

4851 

4875  4900  4924 

4949   4973 

88.2 

2  5  710  12 

1.8 

4973 

4997 

5021 

5045  5068 

5092 

5115  5139  5162 

5185   5208 

88.1 

2  5  7  912 

1.9 

5208 

5231 

5253 

5276  5298 

5321 

5343  5365  5387 

5409  2.5431 

m°m 

2  4  7  911 

2°.0 

2.5431 

5453 

5474 

5496  5517 

5538 

5559  5580  5601 

5622   5643 

87.9 

2  4  6  811 

2.1 

5643 

5664 

5684 

5705  5725 

5745 

5765  5785  5805 

5825   5845 

87.8 

2  4  6  810 

2.2 

5845 

5*865 

5884 

5904  5923 

5943 

5962  5981  6000 

6019   6038 

87.7 

2  4  6  810 

2.3 

6038 

6057 

6076 

6095  6113 

6132 

6150  6169  6187 

6205   6223 

87.6 

2  4  6  7  9 

2.4 

6223 

6242 

6260 

6277  6295 

6313 

6331  6348  6366 

6384   6401 

87.5 

2  4  5  7  9 

2.5 

6401 

6418 

6436 

6453  6470 

6487 

6504  6521  6538 

6555   6571 

87.4 

2  3  5  7  9 

2.6 

6571 

6588 

6605 

6621  6638 

6654 

6671  6687  6703 

6719   6736 

87.3 

2  3  5  7  8 

2.7 

6736 

6752 

6768 

6784  6800 

6815 

6831  6847  6863 

6878   6894 

87.2 

2  3  5  6  8 

2.8 

6894 

6909 

6925 

6940  6956 

6971 

6986  7001  7016 

7031   7046 

87.1 

2  3  5  6  8 

2.9 

7046 

7061 

7076 

7091  7106 

7121 

7136  7150  7165 

7179  2.7194 

87°.© 

13  4  6  7 

3°0 

2-7194 

7208 

7223 

7237  7252 

7266 

7280  7294  7308 

7323   7337 

86.9 

13  4  6  7 

3.1 

7337 

7351 

7365 

7379  7392 

7406 

7420  7434  7448 

7461   7475 

86.8 

13  4  6  7 

3.2 

7475 

7488 

7502 

7515  7529 

7542 

7556  7569  7582 

7596   7609 

86.7 

13  4  5  7 

3.3 

7609 

7622 

7635 

7648  7661 

7674 

7687  7700  7713 

7726  7739 

86.6 

13  4  5  6 

3.4 

7739 

7751 

7764 

7777  7790 

7802 

7815  7827  7840 

7852   7865 

86.5 

13  4  5  6 

3.5 

7865 

7877 

7890 

7902  7914 

7927 

7939  7951  7963 

7975   7988 

86.4 

12  4  5  6 

3.6 

7988 

8000 

8012 

8024  8036 

8048 

8059  8071  8083 

8095   8107 

86.3 

12  4  5  6 

3.7 

8107 

8119 

8130 

8142  8154 

8165 

8177  8188  8200 

8212   8223 

86.2 

12  3  5  6 

3.8 

8223 

8234 

8246 

8257  8269 

8280 

8291  8302  8314 

8325   8336 

86.1 

12  3  5  6 

3.9 

8336 

8347 

8358 

8370  8381 

8392 

8403  8414  8425 

8436  2.8446 

8S°.(D) 

12  3  4  6 

4°.0 

2.8446 

8457 

8468 

8479  8490 

8501 

8511  8522  8533 

8543   8554 

85.9 

12  3  4  5 

4.1 

8554 

8565 

8575 

8586  8596 

8607 

8617  8628  8638 

8649   8659 

85.8 

12  3  4  5 

4.2 

8659 

8669 

8680 

8690  8700 

8711 

8721  8731  8741 

8751   8762 

85.7 

12  3  4  5 

4.3 

8762 

8772 

8782 

8792  8802 

8812 

8822  8832  8842 

8852   8862 

85.6 

12  3  4  5 

4.4 

8862 

8872 

8882 

8891  8901 

8911 

8921  8931  8940 

8950   8960 

85.5 

12  3  4  5 

4.5 

8960 

8970 

8979 

8989  8998 

9008 

9018  9027  9037 

9046   9056 

85.4 

12  3  4  5 

4.6 

9056 

9065 

9075 

9084  9093 

9103 

9112  9122  9131 

9140   9150 

85.3 

12  3  4  5 

4.7 

9150 

9159 

9168 

9177  9186 

9196 

9205  9214  9223 

9232   9241 

85.2 

12  3  4  5 

4.8 

9241 

9250 

9260 

9269  9278 

9287 

9296  9305  9313 

9322   9331 

85.1 

12  3  4  4 

4.9 

9331 

9340 

9349 

9358  9367 

9376 

9384  9393  9402 

9411  2.9420  @S°.(D 

12  3  4  4 

*  When  x  is  between  0°  and  l°.l 
log  tan  x  =  log  rad  x 


[See  page  28] 
(22)  .. 


*  When  x  is  between  88°.9  and  90° 
log  ctn  x  —  log  rad  (90°— x) 


Log 

Tan 

Log  Coft&n 

5°.0 

0 

g) 

_jr 

1 

<s 

s 

5 

4 

6 

a 

7 

8 

1  © 

"~9  1 

84.9 

1 

2 

3 

4 

2.9420 

9428 

9437 

9446 

9454 

9463 

9472 

9480 

9489 

9497  2.9506 

5.1 

9506 

9515 

9523 

9532 

9540 

9549 

9557 

9565 

9574 

9582   9591 

84.8 

5.2 

9591 

9599 

9608 

9616 

9624 

9633 

9641 

9649 

9657 

9666   9674 

84.7 

5.3 

9674 

9682 

9690 

9699 

9707 

9715 

9723 

9731 

9739 

9747  9756 

84.6 

5.4 

9756 

9764 

9772 

9780 

9788 

9796 

9804 

9812 

9820 

9828   9836 

84.5 

5.5 

9836 

9844 

9852 

9860 

9867 

9875 

9883 

9891 

9899 

9907   9915 

84.4 

5.6 

9915 

9922 

9930 

9938 

9946 

9953 

9961 

9969 

9977 

9984  2.9992 

84.3 

5.7 

2.9992  J 

'  0000 

0007 

0015 

0022 

0030 

0038 

0045 

0053 

0060  1.0068 

84.2 

5.8 

T.0068 

0075 

0083 

0090 

0098 

0105 

0113 

0120 

0128 

0135   0143 

84.1 

5.9 

0143 

0150 

0157 

0165 

0172 

0180 

0187 

0194 

0202 

0209  T.0216 

84°.© 

6°0 

1.0216 

0223 

0231 

0238 

0245 

0253 

0260 

0267 

0274 

0281   0289 

83.9 

6.1 

0289 

0296 

0303 

0310 

0317 

0324 

0331 

0338 

0346 

0353   0360 

83.8 

6.2 

0360 

0367 

0374 

0381 

0388 

0395 

0402 

0409 

0416 

0423   0430 

83.7 

6.3 

0430 

0437 

0444 

0451 

0457 

0464 

0471 

0478 

0485 

0492   0499 

83.6 

6.4 

0499 

0506 

0512 

0519 

0526 

0533 

0540 

0546 

0553 

0560   0567 

83.5 

6.5 

0567 

0573 

0580 

0587 

0593 

0600 

0607 

0614 

0620 

0627   0633 

83.4 

6.6 

0633 

0640 

0647 

0653 

0660 

0667 

0673 

0680 

0686 

0693   0699 

83.3 

6.7 

0699 

0706 

0712 

0719 

0725 

0732 

0738 

0745 

0751 

0758   0764 

83.2 

6.8 

0764 

0771 

0777 

0784 

0790 

0796 

0803 

0809 

0816 

0822   0828 

83.1 

6.9 

0828 

0835 

0841 

0847 

0854 

0860 

0866 

0873 

0879 

0885  1.0891 

83°.© 

7°.0 

T.0891 

0898 

0904 

0910 

0916 

0923 

0929 

0935 

0941 

0947  0954 

82.9 

7.1 

0954 

0960 

0966 

0972 

0978 

0984 

0991 

0997 

1003 

1009   1015 

82.8 

7.2 

1015 

1021 

1027 

1033 

1039 

1045 

1051 

1058 

1064 

1070   1076 

82.7 

7.3 

1076 

1082 

1088 

1094 

1100 

1106 

1112 

1117 

1123 

1129   1135 

82.6 

7.4 

1135 

1141 

1147 

1153 

1159 

1165 

1171 

1177 

1183 

1188   1194 

82.5 

7.5 

1194 

1200 

1206 

1212 

1218 

1223 

1229 

1235 

1241 

1247   1252 

82.4 

7.6 

-  1252 

1258 

1264 

1270 

1276 

1281 

1287 

1293 

1299 

1304   1310 

82.3 

7.7 

1310 

1316 

1321 

1327 

1333 

1338 

1344 

1350 

1355 

1361   1367 

82.2 

7.8 

1367 

1372 

1378 

1384 

1389 

1395 

1400 

1406 

1412 

1417   1423 

82.1 

7.9 

1423 

1428 

1434 

1439 

1445 

1450 

1456 

1461 

1467 

1473  1.1478 

82°.© 

8°.0 

1.1478 

1484 

1489 

1494 

1500 

1505 

1511 

1516 

1522 

1527   1533 

81.9 

8.1 

1533 

1538 

1544 

1549 

1554 

1560 

1565 

1571 

1576 

1581   1587 

81.8 

8.2 

1587 

1592 

1597 

1603 

1608 

1613 

1619 

1624 

1629 

1635   1640 

81.7 

8.3 

1640 

1645 

1651 

1656 

1661 

1667 

1672 

1677 

1682 

1688   1693 

81.6 

8.4 

1693 

1698 

1703 

1709 

1714 

1719 

1724 

1729 

1735 

1740   1745 

81.5 

8.5 

1745 

1750 

1755 

1761 

1766 

1771 

1776 

1781 

1786 

1791   1797 

81.4 

8.6 

1797 

1802 

1807 

1812 

1817 

1822 

1827 

1832 

1837 

1842   1848 

81.3 

8.7 

1848 

1853 

1858 

1863 

1868 

1873 

1878 

1883 

1888 

1893   1898 

81.2 

8.8 

1898 

1903 

1908 

1913 

1918 

1923 

1928 

1933 

1938 

1943   1948 

81.1 

8.9 

1948 

1953 

1958 

1963 

1968 

1973 

1977 

1982 

1987 

1992  1.1997 

81°.© 

9°0 

1.1997 

2002 

2007 

2012 

2017 

2022 

2026 

2031 

2036 

2041   2046 

80.9 

9.1 

2046 

2051 

2056 

2060 

2065 

2070 

2075 

2080 

2085 

2089   2094 

80.8 

9.2 

2094 

2099 

2104 

2109 

2113 

2118 

2123 

2128 

2132 

2137   2142 

80.7 

9.3 

2142 

2147 

2151 

2156 

2161 

2166 

2170 

2175 

2180 

2185   2189 

80.6 

9.4 

2189 

2194 

2199 

2203 

2208 

2213 

2217 

2222 

2227 

2231   2236 

80.5 

9.5 

2236 

2241 

2245 

2250 

2255 

2259 

2264 

2269 

2273 

2278   2282 

80.4 

9.6 

2282 

2287 

2292 

2296 

2301 

2305 

2310 

2315 

2319 

2324   2328 

80.3 

9.7 

2328 

2333 

2337 

2342 

2346 

2351 

2356 

2360 

2365 

2369   2374 

80.2 

9.8 

2374 

2378 

2383 

2387 

2392 

2396 

2401 

2405 

2410 

2414   2419 

80.1 

9.9 

1.2419 

2423 

2428 

2432 

2437 

2441 

2445 

2450 

2454 

2459  1.2463 

8©°© 

(23) 


Tenths  of  the 
abular  Difference 
2  3  4  5 


2  3  3  4 

2  3  3  4 

2  2  3  4 

2  2  3  4 

2  2  3  4 

2  2  3  4 

2  2  3  4 

2  2  3  4 

12  3  4 

12  3  4 

12  3  4 

12  3  4' 

12  3  4 

12  3  3 

12  3  3 

12  3  3 

12  3  3 

12  3  3 

12  3  3 

12  3  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

0  112  2 

0  112  2 


0  1 

0  1 

0  1 

0  1 

0  1 


12  2 

12  2 

12  2 

12  2 

12  2 


0  112  2 

0  112  2 

0  112  2 

0  112  2 

0  112  2 


3 

2 


&3 
« 

o 


W 


1* 


S 


/log  tan  a  log  ctn\ 


t  l.l 

Log  Tan 

A 

LOG 

\ -„L?S..5!r.5.L'?9.?.?? 

l. > 

hog  Coftam 

0*'             ' 

^5 

.0 

i  .®   -?a   ^ 

1  2  a 

M 

4 

5 

.4 

.6 

.7 

"T" 

J   B 

~  .9  1 

90° 

Tenths  of  the 
Tabular  Difference 

12  3  4  5 

—  00 

c4V 

0° 

1 

—  00 

2.2419 

3.2419  5429 
2833  3211 

7190 
3559 

8439 
3881 

9409 
4181 

J  0200 
4461 

0870 
4725 

1450 
4973 

1962  2.2419 
5208   5431 

89 
88 

To  avoid  interpo- 
lation in  the  first 
ten  lines  use  the 
special  table  on  tbe 
preceding  page. 

2 

5431 

5643  5845 

6038 

6223 

6401 

6571 

6736 

6894 

7046   7194 

87 

3 

7194 

7337  7475 

7609 

7739 

7865 

7988 

8107 

8223 

8336   8446 

86 

4 

8446 

8554  8659 

8762 

8862 

8960 

9056 

9150 

9241 

9331  2.9420 

85 

5 

2.9420 

9506  9591 

9674 

9756 

9836 

9915 

9992  J  0068 

0143  1.0216 

;  84 

(Ordinary  inter- 

6 

1.0216 

0289  0360 

0430 

0499 

0567 

0633 

0699 

0764 

0828   0891 

83 

polation  would  not 

s»5 

7 

0891 

0954  1015 

1076 

1135 

1194 

1252 

1310 

1367 

1423   1478 

82 

be  accurate  in  the 

8 

1478 

1533  1587 

1640 

1693 

1745 

1797 

1848 

1898 

1948   1997 

81 

first  three  lines.) 

9 

1997 

2046  2094 

2142 

2189 

2236 

2282 

2328 

2374 

2419  T.2463 

80° 

r~ 

10° 

1.2463 

2507  2551 

2594 

2637 

2680 

2722 

2764 

2805 

2846   2887 

79 

4  8  13  17  21 

11 

2887 

2927  2967 

3006 

3046 

3085 

3123 

3162 

3200 

3237   3275 

78 

4  8  12  16  19 

12 

3275 

3312  3349 

3385 

3422 

3458 

3493 

3529 

3564 

3599   3634 

77 

4  7111418 

13 

3634 

3668  3702 

3736 

3770 

3804 

3837 

3870 

3903 

3935   3968 

76 

3  710  13  17 

14 

3968 

4000  4032 

4064 

4095 

4127 

4158 

4189 

4220 

4250   4281 

75 

3  6  9  13  16 

15 

4281 

4311  4341 

4371 

4400 

4430 

4459 

4488 

4517 

4546  4575 

74 

3  6  9  1215 

16 

4575 

4603  4632 

4660 

4688 

4716 

4744 

4771 

4799 

4826   4853 

73 

3  6  8  1114 

J,06 

17 

4853 

4880  4907 

4934 

4961 

4987 

5014 

5040 

5066 

5092   5118 

72 

3  5  8  1113 

18 

5118 

5143  5169 

5195 

5220 

5245 

5270 

5295 

5320 

5345   5370 

71 

3  5  8  10  13 

19 

5370 

5394  5419 

5443 

5467 

5491 

5516 

5539 

5563 

5587  1.5611 

70° 

2  5  710  12 

s'11 

$* 

20° 

1.5611 

5634  5658 

5681 

5704 

5727 

5750 

5773 

5796 

5819   5842 

69 

2  5  710  12 

21 

5842 

5864  5887 

5909 

5932 

5954 

5976 

5998 

6020 

6042   6064 

68 

2  4  7  911 

22 

6064 

6086  6108 

6129 

6151 

6172 

6194 

6215 

6236 

6257   6279 

67 

2  4  6  911 

23 

6279 

6300  6321 

6341 

6362 

6383 

6404 

6424 

6445 

6465   6486 

66 

2  4  6  810 

24 

6486 

6506  6527 

6547 

6567 

6587 

6607 

6627 

6647 

6667   6687 

65 

2  4  6  810 

25 

6687 

6706  6726 

6746 

6765 

6785 

6804 

6824 

6843 

6863   6882 

64 

2  4  6  810 

26 

6882 

6901  6920 

6939 

6958 

6977 

6996 

7015 

7034 

7053   7072 

63 

2  4  6  8  9 

27 

7072 

7090  7109 

7128 

7146 

7165 

7183 

7202 

7220 

7238   7257 

62 

2  4  6  7  9 

28 

7257 

7275  7293 

7311 

7330 

7348 

7366 

7384 

7402 

7420   7438 

61 

2  4  5  7  9 

29 

7438 

7455  7473 

7491 

7509 

7526 

7544 

7562 

7579 

7597  1.7614 

(SO0 

2  4  5  7  9 

30° 

1.7614 

7632  7649 

7667 

7684 

7701 

7719 

7736 

7753 

7771   7788 

59 

2  3  5  7  9 

31 

7788 

7805  7822 

7839 

7856 

7873 

7890 

7907 

7924 

7941   7958 

58 

2  3  5  7  9 

32 

7958 

7975  7992 

8008 

8025 

8042 

8059 

8075 

8092 

8109   8125 

57 

2  3  5  7  8 

33 

8125 

8142  8158 

8175 

8191 

8208 

8224 

8241 

8257 

8274   8290 

56 

2  3  5  7  8 

34 

8290 

8306  8323 

8339 

8355 

8371 

8388 

8404 

8420 

8436   8452 

55 

2  3  5  6  8 

\ 

35 

8452 

8468  8484 

8501 

8517 

8533 

8549 

8565 

8581 

8597   8613 

54 

2  3  5  6  8 

36 

8613 

8629  8644 

8660 

8676 

8692 

8708 

8724 

8740 

8755   8771 

53 

2  3  5  6  8 

37 

8771 

8787  8803 

8818 

8834 

8850 

8865 

8881 

8897 

8912   8928 

52 

2  3  5  6  8 

38 

8928 

8944  8959 

8975 

8990 

9006 

9022 

9037 

9053 

9068   9084 

51 

2  3  5  6  8 

39 

9084 

9099  9115 

9130 

9146 

9161 

9176 

9192 

9207 

9223  1.9238 

50° 

2  3  5  6  8 

40° 

1.9238 

9254  9269 

9284 

9300 

9315 

9330 

9346 

9361 

9376   9392 

49 

2  3  5  6  8 

41 

9392 

9407  9422 

9438 

9453 

9468 

9483 

9499 

9514 

9529   9544 

48 

2  3  5  6  8 

42 

9544 

9560  9575 

9590 

9605 

9621 

9636 

9651 

9666 

9681   9697 

47 

2  3  5  6  8 

43 

9697 

9712  9727 

9742 

9757 

9772 

9788 

9803 

9818 

9833  1.9848 

46 

2  3  5  6  8 

44 

T.9848 

9864  9879 

9894 

9909 

9924 

9939 

9955 

9970 

9985J0.0000 

4S° 

2  3  5  6  8 

45° 

0.0000 

(24) 


Log  Tan 

Log  Coftami 

JQ 

L  * 

.$ 

.1 

3 

A 

5 

.4 

.6 

~!*~ 

1 

M 

45° 

1 

2 

0.0000 

45° 

0.0000 

0015 

0030 

0045 

0061 

0076 

0091 

0106 

0121 

0136 

0152 

44 

46 

0152 

0167 

0182 

0197 

0212 

0228 

0243 

0258 

0273 

0288 

0303 

43 

47 

0303 

0319 

0334 

0349 

0364 

0379 

0395 

0410 

0425 

0440 

0456 

42 

48 

0456 

0471 

0486 

0501 

0517 

0532 

0547 

0562 

0578 

0593 

0608 

41 

49 

0608 

0624 

0639 

0654 

0670 

0685 

0700 

0716 

0731 

0746 

0.0762 

4€)° 

50° 

0.0762 

0777 

0793 

0808 

0824 

0839 

0854 

0870 

0885 

0901 

0916 

39 

51 

0916 

0932 

0947 

0963 

0978 

0994 

1010 

1025 

1041 

1056 

1072 

38 

52 

1072 

1088 

1103 

1119 

1135 

1150 

1166 

1182 

1197 

1213 

1229 

37 

53 

1229 

1245 

1260 

1276 

1292 

1308 

1324 

1340 

1356 

1371 

1387 

36 

54 

1387 

1403 

1419 

1435 

1451 

1467 

1483 

1499 

1516 

1532 

1548 

35 

55 

1548 

1564 

1580 

1596 

1612 

1629 

1645 

1661 

1677 

1694 

1710 

34 

56 

1710 

1726 

1743 

1759 

1776 

1792 

1809 

1825 

1842 

1858 

1875 

33 

57 

1875 

1891 

1908 

1925 

1941 

1958 

1975 

1992 

2008 

2025 

2042 

32 

58 

2042 

2059 

2076 

2093 

2110 

2127 

2144 

2161 

2178 

2195 

2212 

31 

59 

2212 

2229 

2247 

2264 

2281 

2299 

2316 

2333 

2351 

2368  0.2386 

3©° 

60° 

0.2386 

2403 

2421 

2438 

2456 

2474 

2491 

2509 

2527 

2545 

2562 

29 

61 

2562 

2580 

2598 

2616 

2634 

2652 

2670 

2689 

2707 

2725 

2743 

28 

62 

2743 

2762 

2780 

2798 

2817 

2835 

2854 

2872 

2891 

2910 

2928 

27 

63 

2928 

2947 

2966 

2985 

3004 

3023 

3042 

3061 

3080 

3099 

3118 

26 

64 

3118 

3137 

3157 

3176 

3196 

3215 

3235 

3254 

3274 

3294 

3313 

25 

65 

3313 

3333 

3353 

3373 

3393 

3413 

3433 

3453 

3473 

3494 

3514 

24 

66 

3514 

3535 

3555 

3576 

3596 

3617 

3638 

3659 

3679 

3700 

3721 

23 

67 

3721 

3743 

3764 

3785 

3806 

3828 

3849 

3871 

3892 

3914 

3936 

22 

68 

3936 

3958 

3980 

4002 

4024 

4046 

4068 

4091 

4113 

4136 

4158 

21 

69 

4158 

4181 

4204 

4227 

4250 

4273 

4296 

4319 

4342 

4366 

0.4389 

20° 

70° 

0.4389 

4413 

4437 

4461 

4484 

4509 

4533 

4557 

4581 

4606 

4630 

19 

71 

4630 

4655 

4680 

4705 

4730 

4755 

4780 

4805 

4831 

4857 

4882 

18 

72 

4882 

4908 

4934 

4960 

4986 

5013 

5039 

5066 

5093 

5120 

5147 

17 

73 

5147 

5174 

5201 

5229 

5256 

5284 

5312 

5340 

5368 

5397 

5425 

16 

74 

5425 

5454 

5483 

5512 

5541 

5570 

5600 

5629 

5659 

5689 

5719 

15 

75 

5719 

5750 

5780 

5811 

5842 

5873 

5905 

5936 

5968 

6000 

6032 

14 

76 

6032 

6065 

6097 

6130 

6163 

6196 

6230 

6264 

6298 

6332 

6366 

13 

77 

6366 

6401 

6436 

6471 

6507 

6542 

6578 

6615 

6651 

0688 

6725 

12 

78 

6725 

6763 

6800 

6838 

6877 

6915 

6954 

6994 

7033 

7073 

7113 

11 

79 

7113 

7154 

7195 

7236 

7278 

7320 

7363 

7406 

7449 

7493  0.7537 

10° 

80° 

0.7537 

7581 

7626 

7672 

7718 

7764 

7811 

7858 

7906 

7954 

8003 

9 

81 

8003 

8052 

8102 

8152 

8203 

8255 

8307 

8360 

8413 

8467 

8522 

8 

82 

8522 

8577 

8633 

8690 

8748 

8806 

8865 

8924 

8985 

9046 

9109 

7 

83 

9109 

9172 

9236 

9301 

9367 

9433 

9501 

9570 

9640 

9711 

0.9784 

6 

84 

0.9784 

9857 

9932J0008 

0085 

0164 

0244 

0326 

0409 

0494 

1.0580 

5 

85 

1.0580 

0669 

0759 

0850 

0944 

1040 

1138 

1238 

1341 

1446 

1554 

4 

86 

1554 

1664 

1777 

1893 

2012 

2135 

2261 

2391 

2525 

2663 

2806 

3 

87 

2806 

2954 

3106 

3264 

3429 

3599 

3777 

3962 

4155 

4357 

4569 

2 

88 

4569 

4792 

5027 

5275 

5539 

5819 

6119 

6441 

6789 

7167 

1.7581 

1 

89 

1.7581 

8038 

8550 

9130 

9800J 

2.0591 

1561 

2810 

4571 

7581 

00 

0° 

90° 

oo 

(25) 


Tenths  of  the 
Tabular  Difference 

12  3  4  5 


2  3    5    6    8 

2  3    5    6    8 

2  3    5    6    8 

2  3    5    6    8 

2  3    5    6    8 

2  3    5    6    8 

2  3    5    6    8 

2  3    5    6    8 

2  3    5    6    8 

2  3    5    6    8 

2  3    5    6   8 

2  3    5    7    8 

2  3    5    7    8 

2  3    5    7    9 

2  3    5    7    9 

2  4    5    7    9 

2  4    5    7   9 

2  4    6    7    9 

2  4    6    8    9 

2  4    6    810 

2  4    6    810 

2  4    6    810 

2  4    6    911 

2  4    7    911 

2  5    710  12 

2  5  710  12 

3  5  8  10  13 
3  5  8  11  13 
3  6  8  11 14 
3  6  9  12  15 

3  6  9  13  16 

3  710  13  17 

4  7  11  14  18 
4  8  12  16  19 
4  8  13  17  21 

To  avoid  interpo- 
lation in  the  last 
ten  lines,  use  the 
special  table  on  the 


(Ordinary  inter- 
polation would  not 
be  accurate  in  the 
last  three  lines.) 


a* 


&3 
O 
w 

-J 

o 
o 

en 

3 


|o<J 


f* 


u 


LOG 


\  L°£s!n&j6g.cos: J 


Log  Tan 

Log  Coftana 

80°0 

0 

L  ® 

1 

23 

6 

4 

5 

4 

% 

""if— 

1 

9  ~ 

® 

9.9 

6 

7 

0.7537 

7541 

7546  7550 

7555 

7559 

7563 

7568 

7572 

7577 

0.7581 

80.1 

7581 

7586 

7590  7595 

7599 

7604 

7608 

7613 

7617 

7622 

7626 

9.8 

80.2 

7626 

7631 

7635  7640 

7644 

7649 

7654 

7658 

7663 

7667 

7672 

9.7 

80.3 

7672 

7676 

7681  7685 

7690 

7695 

7699 

7704 

7708 

7713 

7718 

9.6 

80.4 

7718 

7722 

7727  7731 

7736 

7741 

7745 

7750 

7755 

7759 

7764 

9.5 

80.5 

7764 

7769 

7773  7778 

7783** 

7787 

7792 

7797 

7801 

7806 

7811 

9.4 

80.6 

7811 

7815 

7820  7825 

7830 

7834 

7839 

7844 

7849 

7853 

7858 

9.3 

80.7 

7858 

7863 

7868  7872 

7877 

7882 

7887 

7891 

7896 

7901 

7906 

9.2 

80.8 

7906 

7911 

7915  7920 

7925 

7930 

7935 

7940 

7944 

7949 

7954 

9.1 

80.9 

7954 

7959 

7964  7969 

7974 

7978 

7983 

7988 

7993 

7998 

0.8003 

9°.© 

81°.0 

0.8003 

8008 

8013  8018 

8023 

8027 

8032 

8037 

8042 

8047 

8052 

8.9 

81.1 

8052 

8057 

8062  8067 

8072 

8077 

8082 

8087 

8092 

8097 

8102 

8.8 

81.2 

8102 

8107 

8112  8117 

8122 

8127 

8132 

8137 

8142 

8147 

8152 

8.7 

81.3 

8152 

8158 

8163  8168 

8173 

8178 

8183 

8188 

8193 

8198 

8203 

8.6 

81.4 

8203 

8209 

8214  8219 

8224 

8229 

8234 

8239 

8245 

8250 

8255 

8.5 

81.5 

8255 

8260 

8265  8271 

8276 

8281 

8286 

8291 

8297 

8302 

8307 

8.4 

81.6 

8307 

8312 

8318  8323 

8328 

8333 

8339 

8344 

8349 

8355 

8360 

8.3 

81.7 

8360 

8365 

8371  8376 

8381 

8387 

8392 

8397 

8403 

8408 

8413 

8.2 

81.8 

8413 

8419 

8424  8429 

8435 

8440 

8446 

8451 

8456 

8462 

8467 

8.1 

81.9 

8467 

8473 

8478  8484 

8489 

8495 

8500 

8506 

8511 

8516  0,8522 

8°.0 

82°.  0 

0.8522 

8527 

8533  8539 

8544 

8550 

8555 

8561 

8566 

8572 

8577 

7.9 

82.1 

8577 

8583 

8588  8594 

8600 

8605 

8611 

8616 

8622 

8628 

8633 

7.8 

82.2 

8633 

8639 

8645  8650 

8656 

8662 

8667 

8673 

8679 

8684 

8690 

7.7 

82.3 

8690 

8696 

8701  8707 

8713 

8719 

8724 

8730 

8736 

8742 

8748 

7.6 

82.4 

8748 

8753 

8759  8765 

8771 

8777 

8782 

8788 

8794 

8800 

8806 

7.5 

82.5 

8806 

8812 

8817  8823 

8829 

8835 

8841 

8847 

8853 

8859 

8865 

7.4 

82.6 

8865 

8871 

8877  8883 

8888 

8894 

8900 

8906 

8912 

8918 

8924 

7.3 

82.7 

8924 

8930 

8936  8942 

8949 

8955 

8961 

8967 

8973 

8979 

8985 

7.2 

82.8 

8985 

8991 

8997  9003 

9009 

9016 

9022 

9028 

9034 

9040 

9046 

7.1 

82.9 

9046 

9053 

9059  9065 

9071 

9077 

9084 

9090 

9096 

9102 

0.9109 

7°.0 

83°.  0 

0.9109 

9115 

9121  9127 

9134 

9140 

9146 

9153 

9159 

9165 

9172 

6.9 

83.1 

9172 

9178 

9184  9191 

9197 

9204 

9210 

9216 

9223 

9229 

9236 

6.8 

83.2 

9236 

9242 

9249  9255 

9262 

9268 

9275 

9281 

9288 

9294 

9301 

6.7 

83.3 

9301 

9307 

9314  9320 

9327 

9333 

9340 

9347 

9353 

9360 

9367 

6.6 

83.4 

9367 

9373 

9380  9386 

9393 

9400 

9407 

9413 

9420 

9427 

9433 

6.5 

83.5 

9433 

9440 

9447  9454 

9460 

9467 

9474 

9481 

9488 

9494 

9501 

6.4 

83.6 

9501 

9508 

9515  9522 

9529 

9536 

9543 

9549 

9556 

9563 

9570 

6.3 

83.7 

9570 

9577 

9584  9591 

9598 

9605 

9612 

9619 

9626 

9633 

9640 

6.2 

83.8 

9640 

9647 

9654  9662 

9669 

9676 

9683 

9690 

9697 

9704 

9711 

6.1 

83.9 

9711 

9719 

9726  9733 

9740 

9747 

9755 

9762 

9769 

9777 

0.9784 

6°.0 

84°.  0 

0.9784 

9791 

9798  9806 

9813 

9820 

9828 

9835 

9843 

9850 

9857 

5.9 

84.1 

9857 

9865 

9872  9880 

9887 

9895 

9902 

9910 

9917 

9925 

0.9932 

5.8 

84.2 

0.9932 

9940 

9947  9955 

9962 

9970 

9978 

9985 

9993  J  0000 

1.0008 

5.7 

84.3 

1.0008 

0016 

0023  0031 

0039 

0047 

0054 

0062 

0070 

0078 

0085 

5.6 

84.4 

0085 

0093 

0101  0109 

0117 

0125 

0133 

0140 

0148 

0156 

0164 

5.5 

84.5 

0164 

0172 

0180  0188 

0196 

0204 

0212 

0220 

0228 

0236 

0244 

5.4 

84.6 

0244 

0253 

0261  0269 

0277 

0285 

0293 

0301 

0310 

0318 

0326 

5.3 

84.7 

0326 

0334 

0343  0351 

0359 

0367 

0376 

0384 

0392 

0401 

0409 

5.2 

84.8 

0409 

0418 

0426  0435 

0443 

0451 

0460 

0468 

0477 

0485 

0494 

5.1 

84.9 

1.0494 

0503 

0511  0520 

0528 

0537 

0546 

0554 

0563 

0572 

1.0580 

s°.o 

Tenths  of  the 
Tabular  Difference 

12  3  4  5 


112  2 

112  2 

112  2 

112  2 


0  112  2 

0  112  2 

0  112  2 

0  112  2 

0  112  2 

0  112  2 


112  2 

112  2 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

12  3  3 

12  3  3 

12  3  3 

12  3  3 

12  3  3 

12  3  3 

12  3  3 

12  3  4 

12  3  4 

12  3  4 

12  3  4 

12  3  4 

2  2  3  4 

2  2  3  4 

2  2  3  4 

2  2  3 

2  2  3 

2  2  3 

2  3  3 

2  3  3 


(26) 


Log  Tan 


Log  Cotai 


85°.0 

85.1 
85.2 
85.3 
85.4 

85.5 
85.6 
85.7 
85.8 
85.9 

86°.0 

86.1 
86.2 
86.3 
86.4 

86.5 
86.6 
86.7 
86.8 
86.9 

87°.0 

87.1 
87.2 
87.3 
87.4 

87.5 
87.6 
87.7 
87.8 
87.9 

88°.0 

88.1 
88.2 
88.3 
88.4 

88.5 
88.6 
88.7 
88.8 
88.9 

89°.  0 

89.1 
89.2 
89.3 
89.4 

89.5 
89.6 
89.7 
89.8 
89.9 


1.0580 
0669 
0759 
0850 
0944 

1040 
1138 
1238 
1341 
1446 

1.1554 
1664 
1777 
1893 
2012 

2135 
2261 
2391 
2525 
2663 

1.2806 
2954 
3106 
3264 
3429 

3599 
3777 
3962 
4155 
4357 

1.4569 
4792 
5027 
5275 
5539 

5819 
6119 
6441 
6789 
7167 

1.7581 
8038 
8550 
9130 

1.9800 

2.0591 
1561 
2810 
4571 

2.7581 


0589  0598  0607  0616  0624 

0678  0687  0695  0704  0713 

0768  0777  0786  0795  0804 

0860  0869  0878  0888  0897 

0954  0963  0973  0982  0992 

1050  1060  1069  1079  1089 

1148  1158  1168  1178  1188 

1249  1259  1269  1279  1289 

1351  1362  1372  1383  1393 

1457  1467  1478  1489  1499 

1564  1575  1586  1597  1608 

1675  1686  1698  1709  1720 

1788  1800  1812  1823  1835 

1905  1917  1929  1941  1952 

2025  2037  2049  2061  2073 

2148  2160  2173  2185  2198 

2274  2287  2300  2313  2326 

2404  2418  2431  2444  2458 

2539  2552  2566  2580  2594 

2677  2692  2706  2720  2734 

2821  2835  2850  2864  2879 

2969  2984  2999  3014  3029 

3122  3137  3153  3169  3185 

3281  3297  3313  3329  3346 

3445  3462  3479  3496  3513 

3616  3634  3652  3669  3687 

3795  3813  3831  3850  3868 

3981  4000  4019  4038  4057 

4175  4195  4215  4235  4255 

4378  4399  4420  4441  4462 

4591  4613  4635  4657  4679 

4815  4838  4861  4885  4908 

5051  5076  5100  5125  5149 

5301  5327  5353  5379  5405 

5566  5594  5621  5649  5677 

5848  5878  5907  5937  5967 

6150  6182  6213  6245  6277 

6475  6508  6542  6577  6611 

6825  6862  6899  6936  6974 

7206  7246  7287  7328  7369 


7624 
8087 
8605 
9193 
9873 

0679 
1671 
2957 
4794 
8039 


7669  7713 

8136  8186 

8660  8716 

9256  9320 
9947J0022 

0769  0860 

1783  1899 

3110  3268 

5028  5277 

8550  9130 


7758  7804 

8236  8287 

8773  8830 

9386  9452 

0099  0177 

0954  1049 

2018  2140 

3431  3602 

5540  5820 
9800J3.0592 


0633  0642  0651  0660  1.0669 

0722  0731  0740  0750   0759 

0814  0823  0832  0841   0850 

0907  0916  0925  0935   0944 

1002  1011  1021  1030   1040 

1099  1109  1118  1128  1138 

1198  1208  1218  1228  1238 

1300  1310  1320  1331  1341 

1404  1414  1425  1435  1446 

1510  1521  1532  1543  1.1554 

1619  1630  1642  1653  1664 

1731  1743  1754  1766  1777 

1846  1858  1870  1881  1893 

1964  1976  1988  2000  2012 

2086  2098  2110  2123  2135 

2210  2223  2236  2249   2261 

2339  2352  2365  2378   2391 

2471  2485  2498  2512   2525 

2608  2621  2635  2649   2663 

2748  2763  2777  2792  1.2806 

2894  2909  2924  2939  2954 

3044  3060  3075  3091  3106 

3200  3216  3232  3248  3264 

3362  3379  3395  3412  3429 

3530  3547  3564  3582  3599 

3705  3723  3740  3758  3777 

3887  3905  3924  3943  3962 

4077  4096  4116  4135  4155 

4275  4295  4316  4336  4357 

4483  4504  4526  4547  1.4569 

4702  4724  4747  4769  4792 

4932  4955  4979  5003  5027 

5174  5199  5225  5250  5275 

5432  5458  5485  5512  5539 

5705  5733  5762  5790  5819 

5997  6027  6057  6088  6119 

6309  6342  6375  6408  6441 

6646  6682  6717  6753  6789 

7012  7050  7088  7127  7167 

7410  7452  7495  7538  1.7581 

7850  7896  7943  7990  8038 

8338  8390  8443  8496  8550 

8889  8948  9008  9068  9130 

9519  9588  9657  9728  1.9800 

0257  0338  0421  0505  2.0591 

1147  1246  1349  1453   1561 

2266  2396  2530  2668  2810 

3779  3964  4157  4359  4571 

6120  6442  6789  7167  2.7581 

1561  2810  4571  7581    00 


4.9 

4.8 
4.7 
4.6 

4.5 

4.4 
4.3 
4.2 
4.1 

4°.@ 

3.9 
3.8 
3.7 
3.6 
3.5 

3.4 
3.3 
3.2 
3.1 

3°.(Q 

2.9 
2.8 

2.7 
2.6 

2.5 

2.4 
2.3 
2.2 
2.1 

2°.<Q 

1.9 
1.8 
1.7 
1.6 
1.5 

1.4 
1.3 
1.2 
1.1 

1°.<Q 

0.9 

0.8 
0.7 
0,6 
0.5 

0.4 
0.3 
0.2 
0.1 


*  When  x  is  between  88°.9  and  90°       [See  page  28] 
log  tan  x  — — log  rad  (90° — a?)  (27) 


*  When  x  is  between  0°  and  l°.l 
log  ctn  x  = — log  rad  x 


(Ordinary  Inter- 
polation would  not 
be  accurate  In  the 
last  three  lines.) 


Tenths  of  the 

Tabular  Difference 

1  2  3 

4 

5 

12    3 

4 

4 

12   3 

4 

4 

I 

12   3 

4 

5 

=* 

12   3 

4 

5 

s 

12   3 

4 

5 

— '"' 

12   3 

4 

5 



12   3 

4 

5 

^=^= 

12    3 

4 

5 

s^^s 

12    3 

4 

5 

7 

12    3 

4 

5 

12    3 

4 

6 

12    3 

5 

6 

12    3 

5 

6 

12    4 

5 

6 

> 

12   4 

5 

6 

%$L 

13   4 

5 

6 

&>3 

13    4 

5 

6 

13    4 

5 

7 

i-4 

13    4 

6 

7 

m  4 

13    4 

6 

7 

13    4 
2    3    5 

6 
6 

7 
8 

-3  *• 

2    3    5 

6 

8 

O  2 

2    3    5 

7 

8 

53  &3 

2    3    5 

7 

9 

H» 

2    4    5 

7 

9 

CO  rf 

2    4   6 

7 

9 

3  a 

2    4    6 

810 

2    4    6 

810 

2    4    6 
2    4    7 

8  11 
911 

2    5    7 

912 

2    5    71012 

3   5    81113 

3    6    81114 

3    6    912  15 

3    6  10  13  16 

3    710  1417 

4    81115  19 

To  avoid  interpo- 

lation in  the  last 

eleven  lines, 

USB 

note.* 

M 


1* 


These  two  pages  give  the  common  logarithms  of  "  rad  x  "  for  angles  x  between  1°  and  10°. 
Moving  the  decimal  point  n  places  to  the  right  (or  left)  in  the  angle  is  equivalent  to  adding 
n  (or  —  n)  to  the  logarithm.    Thus,  log  rad  0°.0002778  =  2.6856  —  4  =  0.6856  —  6. 

The  abbreviation   rad  x    means  the  radian  measure  of  x,  or  the  ratio  of  arc  to  radius. 


,& 


When  x  is  between  0°  and  l°.l 

When  x  is  between  88°.9  and  90° 

For  angles  x 

log  sin  x   =  log  rad  x 

log  cos  x  =   log  rad  (90°  —  x°) 

near  0°  or  90°  :  — 

log  tan  x   =  log  rad  x 

log  ctn  x  =   log  rad  (90°  —  x°) 

log  ctn  x  —   — log  rad  x 

log  tan  x  =   — log  rad  (90°  —  x°) 

Log  Rad 


r.o 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10  j 

2.2419 

2462 

2505 

2547 

2589 

2631 

2672 

2713 

2753 

2793 

2.2833 

.i 

2833 

2872 

2911 

2950 

2988 

3026 

3063 

3101 

3138 

3174 

3211 

.2 

3211 

3247 

3282 

3318 

3353 

3388 

3422 

3457 

3491 

3525 

3558 

.3 

3558 

3591 

3625 

3657 

3690 

3722 

3754 

3786 

3818 

3849 

3880 

.4 

3880 

3911 

3942 

3972 

4002 

4032 

4062 

4092 

4121 

4151 

4180 

1°.5 

2.4180 

4209 

4237 

4266 

4294 

4322 

4350 

4378 

4405 

4433 

2.4460 

•6 

4460 

4487 

4514 

4541 

4567 

4594 

4620 

4646 

4672 

4698 

4723 

.7 

4723 

4749 

4774 

4799 

4824 

4849 

4874 

4899 

4923 

4947 

4971 

.8 

4971 

4996 

5019 

5043 

5067 

5090 

5114 

5137 

5160 

5183 

5206 

•9 

5206 

5229 

5252 

5274 

5297 

5319 

5341 

5363 

5385 

5407 

5429 

2°.0 

2.5429 

5451 

5472 

5494 

5515 

5536 

5557 

5578 

5599 

5620 

2.5641 

.1 

5641 

5662 

5682 

5703 

5723 

5743 

5763 

5783 

5803 

5823 

5843 

.2 

5843 

5863 

5882 

5902 

5921 

5941 

5960 

5979 

5998 

6017 

6036 

.3 

6036 

6055 

6074 

6092 

6111 

6129 

6148 

6166 

6185 

6203 

6221 

.4 

6221 

6239 

6257 

6275 

6293 

6310 

6328 

6346 

6363 

6381 

6398 

2°.  5 

2.6398 

6416 

6433 

6450 

6467 

6484 

6501 

6518 

6535 

6552 

2.6569 

.6 

6569 

6585 

6602 

6618 

6635 

6651 

6668 

6684 

6700 

6716 

6732 

.7 

6732 

6748 

6764 

6780 

6796 

6812 

6828 

6844 

6859 

6875 

6890 

.8 

6890 

6906 

6921 

6937 

6952 

6967 

6982 

6998 

7013 

7028 

7043 

.9 

7043 

7058 

7073 

7087 

7102 

7117 

7132 

7146 

7161 

7175 

7190 

3°.0 

2.7190 

7204 

7219 

7233 

7248 

7262 

7276 

7290 

7304 

7318 

2.7332 

.1 

7332 

7346 

7360 

7374 

7388 

7402 

7416 

7429 

7443 

7457 

7470 

.2 

7470 

7484 

7497 

7511 

7524 

7538 

7551 

7564 

7578 

7591 

7604 

.3 

7604 

7617 

7630 

7643 

7656 

7669 

7682 

7695 

7708 

7721 

7734 

.4 

7734 

7746 

7759 

7772 

7784 

7797 

7810 

7822 

7835 

7847 

7859 

3°.5 

2.7859 

7872 

7884 

7897 

7909 

7921 

7933 

7945 

7958 

7970 

2.7982 

.6 

7982 

7994 

8006 

8018 

8030 

8042 

8054 

8065 

8077 

8089 

8101 

.7 

8101 

8113 

8124 

8136 

8147 

8159 

8171 

8182 

8194 

8205 

8217 

.8 

8217 

8228 

8239 

8251 

8262 

8273 

8285 

8296 

8307 

8318 

8329 

.9 

8329 

8341 

8352 

8363 

8374 

8385 

8396 

8407 

8418 

8429 

8439 

4°.0 

2.8439 

8450 

8461 

8472 

8483 

8493 

8504 

8515 

8525 

8536 

2.8547 

.1 

8547 

8557 

8568 

8578 

8589 

8599 

8610 

8620 

8631 

8641 

8651 

.2 

8651 

8662 

8672 

8682 

8692 

8703 

8713 

8723 

8733 

8743 

8753 

.3 

8753 

8764 

8774 

8784 

8794 

8804 

8814 

8824 

8834 

8843 

8853 

.4 

8853 

8863 

8873 

8883 

8893 

8902 

8912 

8922 

8932 

8941 

8951 

4°  .5 

2.8951 

8961 

8970 

8980 

8989 

8999 

9008 

9018 

9027 

9037 

2.9046 

.6 

9046 

9056 

9065 

9075 

9084 

9093 

9103 

9112 

9121 

9131 

9140 

.7 

9140 

9149 

9158 

9167 

9177 

9186 

9195 

9204 

9213 

9222 

9231 

8 

9231 

9240 

9249 

9258 

9267 

9276 

9285 

9294 

9303 

9312 

9321 

.9 

9321 

9330 

9338 

9347 

9356 

9365 

9374 

9382 

9391 

9400 

9408 

Tenths  of  the 
Tabular  Difference 

12  3    4  5 

4  8  12  17  21 
4  8  11 15  19 
3  710  14  17 
3    6  10  13  16 

3    6  9  12  15 

3    6  8  1114 

3    5  8  1113 

2    5  7  1012 

2    5  7    9  12 

2    4  7    911 

2    4  6    811 

2    4  6    810 

2    4  6    8  10 

2    4  6    7    9 

2    4  5    7    9 

2    3  5    7    9 

2    3  5    7    8 

2    3  5    6    8 

2    3  5    6    8 

13  4    6    7 

13  4    6    7 

13  4    6    7 

13  4    5    7 

13  4    5    6 

13  4    5    6 

12  4    5    6 

12  4    5    6 

12  3    5    6 

12  3    5    6 

12  3    4    5 

12  3    4    5 

12  3    4    5 

12  3    4    5 

12  3    4    5 

12  3    4    5 

12  3    4    5 

12  3    4    5 

12  3    4    5 

12  3    4    4 

12  3    4    4 


Note;     log  rad  x 


log  (number  of  degrees  in  x)    +  0.2419 
(28) 


Log  Rad 

5°.0 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

2.9408 

9417 

9426 

9434 

9443 

9452 

9460 

9469 

9477 

9486 

2.9494 

.1 

9494 

9503 

9511 

9520 

9528 

9537 

9545 

9554 

9562 

9570 

9579 

.2 

9579 

9587 

9595 

9604 

9612 

9620 

9629 

9637 

9645 

9653 

9662 

.3 

9662 

9670 

9678 

9686 

9694 

9702 

9710 

9719 

9727 

9735 

9743 

A 

9743 

9751 

9759 

9767 

9775 

9783 

9791 

9799 

9807 

9814 

9822 

5°.5 

2.9822 

9830 

9838 

9846 

9854 

9862 

9870 

9877 

9885 

9893 

9901 

.6 

9901 

9908 

9916 

9924 

9932 

9939 

9947 

9955 

9962 

9970 

2.9978 

.7 

29978 

9985 

9993  J  0000 

0008 

0015 

0023 

0031 

0038 

0046 

1.0053 

.8 

1.0053 

0061 

0068 

0075 

0083 

0090 

0098 

0105 

0113 

0120 

0127 

.9 

0127 

0135 

0142 

0149 

0157 

0164 

0171 

0179 

0186 

0193 

0200 

6°.0 

1.0200 

0208 

0215 

0222 

0229 

0236 

0244 

0251 

0258 

0265 

1.0272 

.1 

0272 

0279 

0286 

0293 

0300 

0308 

0315 

0322 

0329 

0336 

0343 

.2 

0343 

0350 

0357 

0364 

0371 

0378 

0385 

0391 

0398 

0405 

0412 

.3 

0412 

0419 

0426 

0433 

0440 

0447 

0453 

0460 

0467 

0474 

0481 

.4 

0481 

0487 

0494 

0501 

0508 

0514 

0521 

0528 

0535 

0541 

0548 

6°.5 

1.0548 

0555 

0561 

0568 

0575 

0581 

0588 

0594 

0601 

0608 

1.0614 

.6 

0614 

0621 

0627 

0634 

0640 

0647 

0654 

0660 

0667 

0673 

0680 

.7 

0680 

0686 

0692 

0699 

0705 

0712 

0718 

0725 

0731 

0737 

0744 

.8 

0744 

0750 

0757 

0763 

0769 

0776 

0782 

0788 

0795 

0801 

0807 

.9 

0807 

0814 

0820 

0826 

0832 

0839 

0845 

0851 

0857 

0864 

0870 

7°.0 

1.0870 

0876 

0882 

0888 

0895 

0901 

0907 

0913 

0919 

0925 

1.0931 

.1 

0931 

0937 

0944 

0950 

0956 

0962 

0968 

0974 

0980 

0986 

0992 

.2 

0992 

0998 

1004 

1010 

1016 

1022 

1028 

1034 

1040 

1046 

1052 

.3 

1052 

1058 

1064 

1070 

1076 

1082 

1088 

1093 

1099 

1105 

1111 

.4 

1111 

1117 

1123 

1129 

1135 

1140 

1146 

1152 

1158 

1164 

1169 

7°.  5 

1.1169 

1175 

1181 

1187 

1192 

1198 

1204 

1210 

1215 

1221 

1.1227 

.6 

1227 

1233 

1238 

1244 

1250 

1255 

1261 

1267 

1272 

1278 

1284 

.7 

1284 

1289 

1295 

1301 

1306 

1312 

1317 

1323 

1329 

1334 

1340 

.8 

1340 

1345 

1351 

1356 

1362 

1367 

1373 

1379 

1384 

1390 

1395 

.9 

1395 

1401 

1406 

1412 

1417 

1422 

1428 

1433 

1439 

1444 

1450 

8°.0 

1.1450 

1455 

1461 

1466 

1471 

1477 

1482 

1488 

1493 

1498 

1.1504 

.1 

1504 

1509 

1514 

1520 

1525 

1530 

1536 

1541 

1546 

1552 

1557 

.2 

1557 

1562 

1567 

1573 

1578 

1583 

1589 

1594 

1599 

1604 

1610 

.3 

1610 

1615 

1620 

1625 

1630 

1636 

1641 

1646 

1651 

1656 

1662 

.4 

1662 

1667 

1672 

1677 

1682 

1687 

1692 

1698 

1703 

1708 

1713 

8°.5 

1.1713 

1718 

1723 

1728 

1733 

1738 

1744 

1749 

1754 

1759 

1.1764 

.6 

1764 

1769 

1774 

1779 

1784 

1789 

1794 

1799 

1804 

1809 

1814 

.7 

1814 

1819 

1824 

1829 

1834 

1839 

1844 

1849 

1854 

1859 

1864 

.8 

1864 

1869 

1873 

1878 

1883 

1888 

1893 

1898 

1903 

1908 

1913 

.9 

1913 

1918 

1922 

1927 

1932 

1937 

1942 

1947 

1952 

1956 

1961 

9°.0 

1.1961 

1966 

1971 

1976 

1980 

1985 

1990 

1995 

2000 

2004 

1.2009 

.1 

2009 

2014 

2019 

2023 

2028 

2033 

2038 

2042 

2047 

2052 

2057 

.2 

2057 

2061 

2066 

2071 

2075 

2080 

2085 

2090 

2094 

2099 

2104 

.3 

2104 

2108 

2113 

2118 

2122 

2127 

2132 

2136 

2141 

2145 

2150 

.4 

2150 

2155 

2159 

2164 

2168 

2173 

2178 

2182 

2187 

2191 

2196 

9°.5 

1.2196 

2201 

2205 

2210 

2214 

2219 

2223 

2228 

2232 

2237 

1.2241 

.6 

2241 

2246 

2251 

2255 

2260 

2264 

2269 

2273 

2278 

2282 

2286 

.7 

2286 

2291 

2295 

2300 

2304 

2309 

2313 

2318 

2322 

2327 

2331 

.8 

2331 

2335 

2340 

2344 

2349 

2353 

2358 

2362 

2366 

2371 

2375 

.9 

2375 

2380 

2384 

2388 

2393 

2397 

2401 

2406 

2410 

2414 

2419 

Tenths  of  the 
abular  Difference 

2  3  4  5 


2  3  3  4 

2  3  3  4 

2  2  3  4 

2  2  3  4 

2  2  3  4 

2  2  3  4 

2  2  3  4 

2  2  3  4 

12  3  4 
12  34 

12  3  4 

12  3  4 

12  3  3 

12  3  3 

12  3  3 

12  3  3 

12  3  3 

12  3  3 

12  3  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

12  2  3 

0  112  2 

0  112  2 

0  112  2 

0  112  2 

0  112  2 

0  112  2 

0  112  2 

0  112  2 

0  112  2 

0  112  2 

0  112  2 

0  112  2 

0  112  2 


a& 


►J 

O 

O 

CO 


w 


r*« 


(29) 


, 


Exponentials 


ft* 


in 


s! 


0° 


sin 

j00K 

*an 


YA 


<* 


1   o< 

eft* 

l4d 


n 

0.00 
.01 
.02 
.03 
.04 

0.05 
.06 
.07 
.08 
.09 

0.10 

.11 

.12 
.13 
.14 

0.15 
.16 
.17 
.18 
.19 

0.20 
.21 
.22 
.23 
.24 

0.25 
.26 
.27 
.28 
.29 

0.30 
.31 
.32 
.33 
.34 

0.35 
.36 
.37 
.38 
.39 

0.40 
.41 
.42 
.43 
.44 

0.45 
.46 
.47 
.48 
.49 

0.50 


1.000 
1.010 
1.020 
1.030 
1.041 
1.051 
1.062 
1.073 
1.083 
1.094 
1.105 
1.116 
1.127 
1.139 
1.150 
1.162 
1.174 
1.185 
1.197 
1.209 
1.221 
1.234 
1.246 
1.259 
1.271 
1.284 
1.297 
1.310 
1.323 
1.336 
1.350 
1.363 
1.377 
1.391 
1.405 
1.419 
1.433 
1.448 
1.462 
1.477 
1.492 
1.507 
1.522 
1.537 
1.553 
1.568 
1.584 
1.600 
1.616 
1.632 
1.649 


0.50 
.51 

.52 
.53 
.54 

0.55 
.56 
.57 
.58 
.59 

0.60 
.61 
.62 
.63 
.64 

0.65 
.66 
.67 
.68 
.69 

0.70 
.71 
.72 
.73 
.74 

0.75 
.76 
.77 
.78 
.79 

0.80 
.81 
.82 
.83 
.84 

0.85 
.86 
.87 
.88 
.89 

0.90 
.91 
.92 
.93 
.94 

0.95 
.96 
.97 
.98 
.99 

1.00 


1.649 
1.665 
1.682 
1.699 
1.716 
1.733 
1.751 
1.768 
1.786 
1.804 
1.822 
1.840 
1.859 
1.878 
1.896 
1.916 
1.935 
1.954 
1.974 
1.994 
2.014 
2.034 
2.054 
2.075 
2.096 
2.117 
2.138 
2.160 
2.181 
2.203 
2.226 
2.248 
2.270 
2.293 
2.316 
2.340 
2.363 
2.387 
2.411 
2.435 
2.460 
2.484 
2.509 
2.535 
2.560 
2.586 
2.612 
2.638 
2.664 
2.691 
2.718 


16 
17 
17 
17 
17 
18 
17 
18 
18 
18 
18 
19 
19 
18 
20 
19 
19 
20 
20 
20 
20 
20 
21 
21 
21 
21 
22 
21 
22 
23 
22 
22 
23 
23 
24 
23 
24 
24 
24 
25 
24 
25 
26 
25 
26 
26 
26 
26 
27 
27 


n 

1.0 

.1 
.2 
.3 
.4 

1.5 
.6 
.7 
.8 
.9 

2.0 
.1 
.2 
.3 
.4 


2, 

3 

3, 

3 

4 

4, 

4 

5, 

6 

6. 

7, 

8, 

9, 

9, 

11, 

2.5  12 

.6  13, 

.7  14 

.8  16 

.9  18 

3.0  20 

.1  22, 

.2  24 

.3  27 

.4  29 

3.5  33 

.6  36 

.7  40 

.8  44 

.9  49 

4.0  54 

.1  60 


4.5  90 


718* 

,004 

320 

669 

,055 

482 

953 

474 

050 

686 

389 

166 

025 

974 

02 

18 

46 

88 

.44 

17 

,09 

20 

,53 

11 

96 

12 

60 

45 

70 

40 

60 

34 

69 

70 

45 

02 


148.4 
403.4 
1097. 
2981. 
8103. 
22026. 

4.810 

23.14 

111.3 

535.5 

2576. 

12392. 

59610. 


5. 

6. 
7. 
8. 
9. 
10. 

7r/2 
2tt/2 
3tt/2 
4tt/2 
Stz/2 
6tt/2 
7tt/2 
8tt/2    286751. 


n 

0.00 
.01 
.02 
.03 
.04 

0.05 
.06 
.07 
.08 
.09 

0.10 

.11 

.12 
.13 
.14 

0.15 
.16 
.17 
.18 
.19 

0.20 
.21 
.22 
.23 
.24 

0.25 
.26 
.27 
.28 
.29 

0.30 
.31 
.32 
.33 
.34 

0.35 
.36 
.37 
.38 
.39 

0.40 
.41 
.42 
.43 
.44 

0.45 
.46 
.47 
.48 
.49 

0.50 


„— n    Sfc 


1.000 


0.990 


,-10 


.980 


.-10 


.970 


.-10 


.961 


-9 


.951 
.942 
.932 
.923 
.914 
.905 
.896 
.887 
.878 
.869 
.861 
.852 
.844 
.835 
.827 
.819 
.811 
.803 
.795 
.787 
.779 
.771 
.763 
.756 
.748 
.741 
.733 
.726 
.719 
.712 
.705 
.698 
.691 
.684 
.677 
.670 
.664 
.657 
.651 
.644 
.638 
.631 
.625 
.619 
.613 
0.607 


-10 
-9 


.-10 


-9 
-9 
-9 
-9 
-9 
-9 
-9 
-8 
-9 


-9 


-8 


-7 


-7 


-7 
-7 
-7 
-7 


-7 


-7 
-6 
-7 
-6 
-6 
-6 


n 

0.50 

.51 
.52 
.53 
.54 

0.55 
.56 
.57 
.58 
.59 

0.60 
.61 
.62 
.63 
.64 

0.65 
.66 
.67 
.68 
.69 

0.70 
.71 
.72 
.73 
.74 

0.75 
.76 
.77 
.78 
.79 

0.80 
.81 
.82 
.83 
.84 

0.85 
.86 
.87 
.88 
.89 

0.90 
.91 
.92 
.93 
.94 

0.95 
.96 
.97 
.98 
.99 

1.00 


.607 
.600 
.595 
.589 
.583 
.577 
.571 
.566 
.560 
.554 
.549 
.543 
.538 
.533 
.527 
.522 
.517 
.512 
.507 
.502 
.497 
.492 
.487 
.482 
.477 
.472 
.468 
.463 
.458 
.454 
.449 
.445 
.440 
.436 
.432 
.427 
.423 
.419 
.415 
.411 
.407 
.403 
.399 
.395 
.391 
.387 
.383 
.379 
.375 
.372 
.368 


-7 
-5 
-6 
-6 
-6 


-6 

-5 
-5 
-5 
-5 
-5 
-5 
-5 
-5 
-5 
-5 
-5 
-4 
-5 
-5 
-4 
-5 
-4 
-5 
-4 
-4 
-5 
-4 
-4 
-4 


-4 
-4 
-4 

-4 
-4 
-4 
-4 
-4 
-4 
-3 
-4 


n 


1.0 

.368* 

.1 

.333 

.2 

.301 

.3 

.273 

.4 

.247 

1.5 

.223 

.6 

.202 

.7 

.183 

.8 

.165 

.9 

.150 

2.0 

.135 

.1 

.122 

.2 

.111 

.3 

.100 

.4 

.0907 

2.5 

.0821 

.6 

.0743 

.7 

.0672 

.8 

.0608 

.9 

.0550 

3.0 

.0498 

.1 

.0450 

.2 

.0408 

.3 

.0369 

.4 

.0334 

3.5 

.0302 

.6 

.0273 

.7 

.0247 

.8 

.0224 

.9 

.0202 

4.0 

.0183 

.1 

.0166 

.2 

.0150 

.3 

.0136 

.4 

.0123 

4.5 

.0111 

5. 

.00674 

6. 

.00248 

7. 

.000912 

8. 

.000335 

9. 

.000123 

10. 

.000045 

tt/2 

.208 

2tt/2 

.0432 

3tt/2 

.00898 

4tt/2 

.00187 

5tt/2 

.000388 

67T/2 

.000081 

7tt/2 

.000017 

87T/2 

.000003 

*  Note  :  Do  not  interpolate  in  third  and  sixth  columns. 

e=2.71828  l/e=0.367879  logIoe=0.4343 

sinhx=i(e*-e-*)  cosh  x=i{e'+e~x)  logIO(0.4343)= 1.6378 

(30) 


l/(0.4343)=2.3026 
logIO(ew)=n(0.4343) 


Moving  the  decimal  point 
&  places  to  the  right  (or  left) 
in  the  number  is  equivalent 
to   adding  fc  times  2.30259 
(or  —  h,  times  2.30259)  to  the 
logarithm. 

k 

loge(10k) 

5 
6 
7 
8 
9 

11.51293 
13.81551 
16.11810 
18.42068 
20.72327 

1 

2 
3 
4 

2.30259 

4.60517 
6.90776 
9.21034 

Loge  (Base  e= 

=2.71828+) 

Tenths  of  the 

0 

1 

2 

3 

4 

5 

6        7        8        9 

10 

Tabular  Difference 

.i 

12    3    4    5 

-2.303     - 

-2.207  - 

2.120  -: 

2.040- 

1.966    - 

-1.897     - 

-1.833  -1.772  -1.715  -1.661     - 

-1.609 

2       96—52 

.2 

-1.609    • 

-1.561  - 

1.514  - 

1.470  - 

1.427    • 

-1.386     - 

-1.347  -1.309  -1.273  -1.238     • 

-1.204 

£       48—34 

.3 

-1.204    - 

-1.171  - 

L.139  - 

L.109  -: 

L.079    - 

-1.050     - 

-1.022  -0.994  -0.968  -0.942     • 

-0.916 

£       33—26 

.4 

-.9163 

-.8916  - 

-.8675  - 

-.8440- 

-.8210 

-.7985 

-.7765  -.7550  -.7340  -.7133 

-.6931 

ig     247—202 

.5 

-.6931 

-.6733  - 

-.6539  - 

-.6349  - 

-.6162 

-.5978 

-.5798  -.5621  -.5447  -.5276 

-.5108 

2     198—168 

.6 

-.5108 

-.4943  - 

-.4780  - 

-.4620  - 

-.4463 

-.4308 

-.4155  -.4005  -.3857  -.3711 

-.3567 

^o     165—144 

.7 

-.3567 

-.3425  - 

-.3285  - 

-.3147  - 

-.3011 

-.2877 

_.2744  -.2614  -.2485  -.2357 

-.2231 

&    142-126 

.8 

-.2231 

-.2107  - 

-.1985  - 

-.1863  - 

-.1744 

-.1625 

-.1508  -.1393  -.1278  -.1165 

-.1054 

9     124—111 

.9 

-.10536 

-.09431 

-.08338 

-.07257 

-.06188 

-.05129 

-.04082-.03046-.02020-.01005 

.00000 

g   1105—1005 

1.00 

.00000 

.00100 

.00200 

.00300 

.00399 

.00499 

.00598  .00698  .00797  .00896 

.00995 

10  20  30  40  50 

1.01 

.00995 

.01094 

.01193 

.01292 

.01390 

.01489 

.01587  .01686  .01784  .01882 

.01980 

10  20  30  39  49 

1.02 

.01980 

.02078 

.02176 

.02274 

.02372 

.02469 

.02567  .02664  .02762  .02859 

.02956 

10  20  29  39  49 

1.03 

.02956 

.03053 

.03150 

.03247 

.03343 

.03440 

.03537  .03633  .03730  .03826 

.03922 

10  19  29  39  48 

1.04 

.03922 

.04018 

.04114 

.04210 

.04306 

.04402 

.04497  .04593  .04688  .04784 

.04879 

10  19  29  38  48 

1.05 

.04879 

.04974 

.05069 

.05164 

.05259 

.05354 

.05449  .05543  .05638  .05733 

.05827 

9  19  28  38  47 

1.06 

.05827 

.05921 

.06015 

.06110 

.06204 

.06297 

.06391  .06485  .06579  .06672 

.06766 

9  19  28  38  47 

1.07 

.06766 

.06859 

.06953 

.07046 

.07139 

.07232 

.07325  .07418  .07511  .07603 

.07696 

9  19  28  37  47 

1.08 

.07696 

.07789 

.07881 

.07973 

.08066 

.08158 

.08250  .08342  .08434  .08526 

.08618 

9  18  28  37  46 

1.09 

.08618 

.08709 

.08801 

.08893 

.08984 

.09075 

.09167  .09258  .09349  .09440 

.09531 

9  18  27  37  46 

1.1 

.0953 

.1044 

.1133 

.1222 

.1310 

.1398 
.1398 

.1484    .1570    .1655    .1740 

.1823 

9  18  27  36  44 
9  17  26  34  43 

1.2 

.1823 

.1906 

.1989 

.2070 

.2151 

.2231 
.2231 

.2311    .2390    .2469    .2546 

.2624 

8  16  24  33  41 
8  16  24  31  39 

1.3 

.2624 

.2700 

.2776 

.2852 

.2927 

.3001 

.3075    .3148    .3221    .3293 

.3365 

7  15  22  30  37 

1.4 

.3365 

.3436 

.3507 

.3577 

.3646 

.3716 

.3784    .3853    .3920    .3988 

.4055 

7  14  21  28  34 

1.5 

.4055 

.4121 

.4187 

.4253 

.4318 

.4383 

.4447    .4511    .4574    .4637 

.4700 

6  13  19  26  32 

1.6 

.4700 

.4762 

.4824 

.4886 

.4947 

.5008 

.5068    .5128    .5188    .5247 

.5306 

6  12  18  24  30 

1.7 

.5306 

.5365 

.5423 

.5481 

.5539 

.5596 

.5653    .5710    .5766    .5822 

.5878 

6  11  17  23  29 

1.8 

.5878 

.5933 

.5988 

.6043 

.6098 

.6152 

.6206    .6259    .6313    .6366 

.6419 

5  11  16  22  27 

1.9 

.6419 

.6471 

.6523 

.6575 

.6627 

.6678 

.6729    .6780    .6831    .6881 

.6931 

5  10  15  21  26 

2.0 

.6931 

.6981 

.7031 

.7080 

.7129 

.7178 

.7227    .7275    .7324    .7372 

.7419 

5  10  15  20  24 

2.1 

.7419 

.7467 

.7514 

.7561 

.7608 

.7655 

.7701    .7747    .7793    .7839 

.7885 

5    9  14  19  23 

2.2 

.7885 

.7930 

.7975 

.8020 

.8065 

.8109 

.8154    .8198    .8242    .8286 

.8329 

4    9  13  18  22 

2.3 

.8329 

.8372 

.8416 

.8459 

.8502 

.8544 

.8587    .8629    .8671    .8713 

.8755 

4    9  13  17  21 

2.4 

.8755 

.8796 

.8838 

.8879 

.8920 

.8961 

.9002    .9042    .9083    .9123 

.9163 

4    8  12  16  20 

2.5 

.9163 

.9203 

.9243 

.9282 

.9322 

.9361 

.9400    .9439    .9478    .9517 

.9555 

4    8  12  16  20 

2.6 

.9555 

.9594  0.9632  0.9670  0.9708 

0.9746 

0.9783  0.9821  0.9858  0.9895 

0.9933 

4    8  11  15  19 

2.7 

0.9933 

0.9969  1.0006  1.0043  1.0080 

1.0116 

1.0152  1.0188  1.0225  1.0260 

1.0296 

4    7  11  15  18 

2.8 

1.0296 

1.0332  1.0367  1.0403  1.0438 

1.0473 

1.0508  1.0543  1.0578  1.0613 

1.0647 

4    7  11  14  18 

2.9 

1.0647 

1.0682  1.0716  1.0750  1.0784 

1.0818 

1.0852  1.0886  1.0919  1.0953 

1.0986 

3    7  10  14  17 

3. 

1.099 

1.131 

1.163 

1.194 

1.224 

1.253 
1.253 

1.281    1.308    1.335    1.361 

1.386 

3  6  9  12  15 
3    5    8  11  13 

4. 

1.386 

1.411 

1.435 

1.459 

1.482 

1.504 
1.504 

1.526    1.548    1.569    1.589 

1.609 

2  5  7  9  12 
2    4    6    8  11 

5. 

1.609 

1.629 

1.649 

1.668 

1.686 

1.705 

1.723    1.740    1.758    1.775 

1.792 

2    4    5    7    9 

6. 

1.792 

1.808 

1.825 

1.841 

1.856 

1.872 

1.887    1.902    1.917    1.932 

1.946 

2    3    5    6    8 

7. 

1.946 

1.960 

1.974 

1.988 

2.001 

2.015 

2.028    2.041    2.054    2.067 

2.079 

13    4    5    7 

8. 

2.079 

2.092 

2.104 

2.116 

2.128 

2.140 

2.152    2.163    2.175    2.186 

2.197 

12    4    5    6 

9. 

2.197 

2.208 

2.219 

2.230 

2.241 

2.251 

2.262    2.272    2.282    2.293 

2.303 

12    3    4    5 

3d 


tf> 


&3  jj 

8U 

O 
O 

2 


loge  10=2.3025851    loge  x=  (2.3026)  logIO  x    (31)   logIO  e=0.4342944S    logIO*=(0.4343)loge  x 


w     I 


Radians 


From  Radians  into  Degrees 


7 

8 

9 
10° 

1 

2 

3 

4 
15 

6 

7 

8 

9 
20° 

1 

2 

3 

4 
25 

6 

7 

8 

9 
30° 

1 

2 

3 

4 
35 

6 

7 

8 

9 
40° 

1 

2 

3 

4 
45 

6 

7 

8 

9 


.0000 
.0175 
.0349 
.0524 
.0698 
.0873 


6   .1047 


.1222 
.1396 
.1571 
.1745 
.1920 
.2094 
.2269 
.2443 
.2618 
.2793 
.2967 
.3142 
.3316 
.3491 
.3665 
.3840 
.4014 
.4189 
.4363 
.4538 
.4712 
.4887 
.5061 
.5236 
.5411 
.5585 
.5760 
.5934 
.6109 
.6283 
.6458 
.6632 
.6807 
.6981 
.7156 
.7330 
.7505 
.7679 
.7854 
.8029 
.8203 
.8378 
.8552 


50°  .8727 


50° 

1 
2 
3 
4 

55 
6 
7 
8 
9 

60° 
1 
2 
3 
4 

65 
6 
7 
8 
9 

70° 
1 
2 
3 
4 

75 
6 
7 
8 
9 

80° 
1 
2 
3 
4 

85 
6 
7 
8 
9 

90° 
1 
2 
3 
4 

95 
6 
7 
8 
9 
100° 


0.8727 
.8901 
.9076 
.9250 
.9425 
.9599 
.9774 
0.9948 
1.0123 
1.0297 
1.0472 
1.0647 
1.0821 
1.0996 
1.1170 
1.1345 
1.1519 
1.1694 
1.1868 
1.2043 
1.2217 
1.2392 
1.2566 
1.2741 
1.2915 
1.3090 
1.3265 
1.3439 
1.3614 
1.3788 
1.3963 
1.4137 
1.4312 
1.4486 
1.4661 
1.4835 
1.5010 
1.5184 
1.5359 
1.5533 
1.5708 
1.5882 
1.6057 
1.6232 
1.6406 
1.6581 
1.6755 
1.6930 
1.7104 
1.7279 
1.7453 


0°.l 

.0017 

.2 

.0035 

.3 

.0052 

.4 

.0070 

.5 

.0087 

.6 

.0105 

.7 

.0122 

.8 

.0140 

.9 

.0157 

0°.01  .0002 

.02  .0003 

.03  .0005 

.04  .0007 

.05  .0009 

.06  .0010 

.07  .0012 

.08  .0014 

.09  .0016 


30°  0.5236=  n/6 
45°  0.7854=  7r/4 
60°  1.0472=  tc/3 


90° 

100 

110 

120° 

130 

135° 

140 

150° 

160 

170 

180° 

190 

200 

210° 

220 

225° 

230 

240° 

250 

260 

270° 

280 

290 

300° 

310 

315° 

320 

330° 

340 

350 

360° 


1.5708 

1.7453 
1.9199 
2.0944 
2.2689 
2.3562 
2.4435 
2.6180 
2.7925 
2.9671 
3.1416 
3.3161 
3.4907 
3.6652 
3.8397 
3.9270 
4.0143 
4.1888 
4.3633 
4.5379 
4.7124 
4.8869 
5.0615 
5.2360 
5.4105 
5.4978 
5.5851 
5.7596 
5.9341 
6.1087 
6.2832 


tt/2 

2tt/3 
3tt/4 

57T/6 


77T/6 
57T/4 

4tt/3 

=  3tt/2 

:  5tt/3 

=    77T/4 
:ll7T/6 

=  2tt 


Multiples  of 
360°  or  27T  radians 


360° 
720° 
1080° 
1440° 
1800° 
2160° 
2520° 

8  2880° 

9  3240° 
10    3600° 


6.28319 
12.56637 
18.84956 
25.13274 
31.41593 
37.69911 
43.98230 
50.26548 
56.54867 
62.83185 


1  radian  =  180°/7T  =  57°.29578 
l°=7r/180  =  0.0174533  radians. 

log  (x  in  radians)  =  log  (x  in  degrees)  +  0.2419 — 2 


0.00 
.01 

.02 
.03 
.04 

0.05 
.06 
.07 
.08 
.09 

0.10 

.11 

.12 
.13 
.14 

0.15 
.16 
.17 
.18 
.19 

0.20 
.21 
.22 
.23 
.24 

0.25 
.26 
.27 
.28 
.29 

0.30 
.31 
.32 
.33 
.34 

0.35 
.36 
.37 
.38 
.39 

0.40 
.41 
.42 
.43 
.44 

0.45 
.46 
.47 
.48 
.49 

0.50 


o°.oo 

0°.57 

1°.15 

1°.72 

2°.29 

2°.  86 

3°.44 

4°.01 

4°.58 

5°.  16 

5°.73 

6°.30 

6°.  88 

7°.45 

8°.02 

8°.59 

9°.  17 

9°.74 

10°.  31 

10°.  89 

11°.46 

12°.03 

12°.61 

13°.18 

13°.75 

14°.32 

14°.90 

15°.47 

16°.04 

16°.62 

17°.  19 

17°.76 

18°.33 

18°.91 

19°.48 

20°.05 

20°.  63 

21°.20 

21°.77 

22°.35 

22°.92 

23°.49 

24°.06 

24°.64 

25°.21 

25°.78 

26°.35 

26°.  93 

27°.50 

28°.07 

28°.65 


1. 

2. 
3. 
4. 
5. 
6. 
7. 
8. 
9. 
10. 


57°.30 
114°.59 
171°.  89 
229°.  18 
286°.48 
343°.77 
401°.07 
458°.37 
515°.66 
572°.96 


0.001 

.002 
.003 
.004 
.005 
.006 
.007 
.008 
.009 


0°.06 
°.ll 
°.17 
°.23 
°.29 
°.34 
°.40 
°.46 
°.52 


0.50 

.51 
.52 
.53 
.54 

0.55 
.56 
.57 
.58 
.59 

0.60 
.61 
.62 
.63 
.64 

0.65 
.66 
.67 
.68 
.69 

0.70 
.71 
.72 
.73 
.74 

0.75 
.76 
.77 
.78 
.79 

0.80 
.81 
.82 
.83 
.84 

0.85 
.86 
.87 
.88 
.89 

0.90 
.91 
.92 
.93 
.94 

0.95 
.96 
.97 
.98 
.99 

1.00 


28°.65 
29°.22 
29°.79 
30°.37 
30°.94 
31°.51 
32°.09 
32°.66 
33°.23 
33°.80 
34°.38 
34°.95 
35°.52 
36°.  10 
36°.67 
37°.24 
37°.82 
38°.39 
38°.96 
39°.53 
40°.  11 
40°.68 
41°.25 
41°.  83 
42°.40 
42°.97 
43°.  5  4 
44°.  12 
44°.  69 
45°.26 
45°.  84 
46°.  41 
46°.98 
47°.  5  6 
48°.  13 
48°.70 
49°.27 
49°.  85 
50°.42 
50°.99 
51°.57 
52°.  14 
5  2°.  70 
53°.29 
53°.86 
5  4°.  43 
55°.00 
55°.58 
56°.15 
56°.72 
57°.30 


0.0001 

.0002 
.0003 
.0004 
.0005 
.0006 
.0007 
.0008 
.0009 


°.01 
°.01 
°.02 
°.02 
°.03 
°.03 
°.04 
°.05 
°.05 


1.00 

.01 

.02 

.03 

.04 
1.05 

.06 

.07 

.08 

.09 
1.10 

.11 

.12 

.13 

.14 
1.15 

.16 

.17 

.18 

.19 
1.20 

.21 

.22 

.23 

.24 
1.25 

.26 

.27 

.28 

.29 
1.30 

.31 

.32 

.33 

.34 
1.35 

.36 

.37 

.38 

.39 
1.40 

.41 

.42 

.43 

.44 
1.45 

.46 

.47 

.48 

.49 
1.50 

.51 

.52 

.53 

.54 
1.55 

.56 
1.57 

1.5708  90° 

3.1416  180° 

4.7124  270° 

6.2832  360c 


log  (x  in  degrees)=log  {x  in  radians) +1.7581 


(32) 


Conden 

sed  T 

able 

of  Tngoi 

lometnc  J 

-•unctions 

Constants 

rad    ^      sin 

tan 

sec  vers  covers  esc 

ctn   cos 

ir=3.14159265 

■ 

ia 

e=2.71828183 

^^^^^™ 

0.0000    0° 

0.0000 

0.0000 

1.000  0.0000 

1.000      oo 

oo       1.000     9©°  1.571 

1  mile=5280  ft. 

oH5 

.0175     1 

.0175 

.0175 

1.000     .0002 

0.983  57.30* 

57.29*  1.000 

89    1.553 

^      i 

.0349     2 

.0349 

.0349 

1.001     .0006 

.965  28.65* 

28.64*  0.999 

88    1.536 

30  mi.  per  hr. 

~~    m 

.0524    3 

.0523 

.0524 

1.001     .0014 

.948   19.11* 

19.08*     .999 

87     1.518 

=44  ft.  per  sec. 

o         =| 

.0698    4 

0.0873     5° 

.0698 
0.0872 

.0699 
0.0875 

1.002     .0024 
1.004  0.0038 

.930  14.34* 
0.913   11.47* 

14.30*     .998 
11.43*  0.996 

86    1.501 

85°  1.484 

1  nautical  mile 
=6080.3  ft. 

iy     =~ 

t| 

^==5 

c 

.1047     6 

.1045 

.1051 

1.006     .0055 

.895     9.57* 

9.51*     .995 

84    1.466 

=1.1516  mi. 

'id 

1 

.1222     7 

.1219 

.1228 

1.008     .0075 

.878     8.21* 

8.14*     .993 

83    1.449 

CJ        — 

t-H 

.1396     8 

.1392 

.1405 

1.010     .0097 

.861     7.19* 

7.12*     .990 

82    1.431 

1  rod=16J  ft. 

en        j 

II 

t-i 

.1571     9 

.1564 

.1584 

1.012     .0123 

.844     6.39* 

6.31*     .988 

81     1.414 

r\Ji^ ™ " 

m 
a-. 

o 

0.1745 10° 

.1920  11 
.2094  12 

0.1736 
.1908 
.2079 

0.1763 
.1944 
.2126 

1.015  0.0152 
1.019     .0184 
1.022     .0219 

0.826     5.76* 
.809     5.24 
.792     4.81 

5.67*  0.985 
5.14      .982 
4.70      .978 

80°  1.396 
79    1.379 
78    1.361 

1  acre 

=160  sq.  rods 

=43560  sq.  ft. 

1X3 

u 

H 

.2269  13 

.2250 

.2309 

1-026     .0256 

.775     4.45 

4.33       .974 

77    1.344 

1  sq.  mile                        / 
=640  acres 

to 
0 

.2443  14 

.2419 

.2493 

1.031     .0297 

.758     4.13 

4.01       .970 

76    1.326 

T 

0.262     15° 

0.259 

0.268 

1.035  0.0341 

0.741     3.86 

3.73     0.966 

75°  1.309 

t-H 

|| 

.279     16 

.276 

.287 

1.040     .0387 

.724     3.63 

3.49      .961 

74    1.292 

1  bushel  (U.  S.)      ' 

H 

.297     17 

.292 

.306 

1.046     .0437 

.708     3.42 

3.27      .956 

73    1.274 

=2150.42  cu.  in. 

.314     18 

.309 

.325 

1.051     .0489 

.691     3.24 

3.08      .951 

72    1.257 

1  gallon  (U.  S.) 
=231  cu.  in. 

f 

.332     19 

.326 

.344 

1.058     .0545 

.674     3.07 

2.90      .946 

71     1.239 

<u 

0.349  20° 

0.342 

0.364 

1.064  0.0603 

0.658     2.92 

2.75     0.940 

7©°  1.222 

lgallon(British) 

13 

.367     21 

.358 

.384 

1.071     .0664 

.642     2.79 

2.61       .934 

69    1.204 

.384     22 

.375 

.404 

1.079     .0728 

.625     2.67 

2.48       .927 

68    1.187 

=277.463  cu.  in.                6J  ■ 

OH 
1  pound  av. 
=7000  grains 

Spec.  grav.  of                  y  S 

(4 

.401     23 

.391 

.424 

1.086     .0795 

.609     2.56 

2.36       .921 

67     1.169 

.O 

>> 

.419     24 
0.436     25° 

.407 
0.423 

.445 
0.466 

1.095     .0865 
1.103  0.0937 

.593     2.46 
0.577     2.37 

2.25       .914 
2.14     0.906 

66    1.152 
65°  1.134 

a! 

£ 

.454     26 

.438 

.488 

1.113     .1012 

.562     2.28 

2.050     .899 

64    1.117 

£. 

.471     27 

.454 

.510 

1.122     .1090 

.546     2.20 

1.963     .891 

63    1.100 

mercury=13.6 

.489     28 

.469 

.532 

1.133     .1171 

.531     2.13 

1.881     .883 

62    1.082 

1  £  s 

13 

.506     29 

.485 

.554 

1.143     .1254 

.515     2.06 

1.804     .875 

61     1.065 

1  cu.  ft.  of  water 

a! 

0.524  30° 

0.500 

0.577 

1.155   0.1340 

0.500     2.00 

1.732  0.866 

(B©°  1.047 

weighs  62.4  lbs. 

1  cu.  ft.  dry  air 
(32°  F„  30  in.) 
weighs  .0807  lbs. 

S 
to 

.541     31 

.515 

.601 

1.167     .1428 

.485     1.942 

1.664     .857 

59     1.030 

g 

.559    32 

.530 

.625 

1.179     .1520 

.470     1.887 

1.600     .848 

58    1.012 

"S 

P. 

.576     33 

.545 

.649 

1.192     .1613 

.4o5     i.836 

1.540     .839 

57    0.995 

.593     34 

.559 

.675 

1.206     .1710 

.441     1.788 

1.483     .829 

56      .977 

c 

0.611    35° 

0.574 

0.700 

1.221  0.1808 

0.426     1.743 

1.428  0.819 

55°  0.960 

Veloc.  of  sound 

.628     36 
.646     37 

.588 
.602 

.727 
.754 

1.236     .1910 
1.252     .2014 

.412     1.701 
.398     1.662 

1.376     .809 
1.327     .799 

54      .942 
53      .925 

in  air 
=1090  ft./sec. 

B. 

.663     38 

.616 

.781 

1.269     .2120 

.384     1.624 

1.280     .788 

52      .908 

Veloc.  of  li°"ht 

C 

.681     39 

.629 

.810 

1.287     .2229 

.371     1.589 

1.235     .777 

51      .890 

in  vacuum= 

0.698  40° 

0.643 

0.839 

1.305  0.234 

0.357     1.556 

1.192  0.766 

50°  0.873 

186  000  mi./sec. 

i 

.716    41 

.656 

.869 

1.325     .245 

.344     1.524 

1.150     .755 

49      .855 

1 

.733     42 

.669 

.900 

1.346     .257 

.331     1.494 

1.111     .743 

48      .838 

Earth's  radii : 

.750    43 

.682 

.933 

1.367     .269 

.318     1.466 

1.072     .731 

47      .820 

3963mi.,3950mi. 

.768     44 

.695 

0.966 

1.390     .281 

.305     1.440 

1.036     .719 

46      .803 

Earth's  density 
(water=l)=5.5 

Diameter  of 

0.785  45° 

0.707 

1.000 

1.414  0.293 

0.293     1.414 

1.000  0.707 

45°  0.785 

C©S 

eta 

csc  covers  veirs  sec 

tela  snira 

M  md 

fc=3 

Sun,  866  000  mi., 
Moon,  2163  mi. 

1  meter=39.37  in. 

=3.2808  ft. 

I  inch=2.5400  cm.        1  ft.=0.3048  m. 

1  kilometer=0.62137  mi. 

L  mile=1.60935  kilometers 

Mass 

1  hectare=10000  sq.  meters=2.471  acres 

L  acre=0.4047  hectares 

(Earth=l): 
Sun,  334  000; 

1  cu.  meter=1.3079  cu.  yds 

L  cu.  yd.=0.76456  cu.  meters 

1  liter=1000  cu.  cm.=0.2642  gal.  (U.  S.) 

1  gallon  (U.  S.) 

=3.785  liters 

Moon,  0.0123 

1  kg.=2.2046  lbs.        1  gm 

.=15.432  grains 

L  lb.=0.4536  kg 

1  erain=0.0648  gm. 

1  kg./sq.  cm.=14.22  lbs./sq.  in.= 

0.968  atmos 

L  lb./sq.  in.=0.0703  kg./sq.  cm.=0.680  atm 

ds    Distance  of 

(1  atmo=1.033  kg./sq.  cm. 

=760  mm.  of  Hg) 

1  atmo=14.70  lbs./sq.  in.=29.92  in.  of  Hg 

)     Sun, 

1  kilogram  meter=7.233  ft.  lbs. 

L  ft.  lb.  =0.1383 

kilogram  meters 

93  000  000  mi., 

1  kilowatt=1.341  horse-power 

L  H.  P.=550  ft.  Ibs7sec.=746  watts 

Moon, 

SM 

81  cm./sec.z= 

=977.99+5.22  sin 

2  flat.) 

7=322  ft./sec.2 

=32.087+0J71 

sin2  (lat.) 

240  000  mi. 

1$ 

